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Cornell University Library 
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Inheritance tax calculations; an explanat 




3 1924 020 038 679 



IV i^ 



Cornell University Law Library 

THE GIFT OF 

Hodgson, Rus 3, All dre 

'."/oods & Goodyear 
80p.Jl..&.,.T.. mdg. ,.j3uf ialp.,.W.^Y.,,. 

Date Sept.erataer. .9,1957 



IOCSTe; feABcocX, SPR.rr ii ,^ 



h tt I, 







''^^HiR^'V^ 




The original of this bool< is in 
the Cornell University Library. 

There are no known copyright restrictions in 
the United States on the use of the text. 



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INHERITANCE TAX CALCULATIONS 



AN EXPLANATION OF THE UNDERLYING PRINCIPLES 
WITH TABLES AND INSTRUCTIONS FOR ASCER- 
TAINING THE PRESENT VALUE OF DOWER 
AND CURTESY RIGHTS, LIFE ESTATES, 
ANNUITIES, VESTED AND CONTIN- 
GENT REMAINDERS 



UPON THB 



NORTHAMPTON, CARLISLE, AMERICAN AOT) ACTUARIES' EXPERI- 
ENCE TABLES OF MORTALITY AT VARIOUS RATES OP INTER- 
EST, WITH A BRIEF ANALYSIS OF THE INHERITANCE TAX 
IjAWS OF THE Vii.RIOUS STATES AND TERRITORIES 



HERBERT -KpLPE, F. S. S. 

COHSUZ«TlNa ACTuS^, HBW TORE CITT 



IfEW YORK 

BAKER, VOORHIS & COMPANY 

1905 



j& 9S£?'^ 



COPTMGHT, 1905, 

B. HBRBEET WOLFE, F. S. S. 



J. H. LYON COMPANY 

PRINTERS AND BINDEBS 

Al^BANY, N, Y, 



PREFACE. 



The Legislatures of the various States have of 
late years devoted considerable attention to acts 
taxing inheritances. At the present time the 
statute books of nearly all of the larger and 
wealthier States contain provisions for the levy- 
ing of a tax of this nature. The number of in- 
quiries which have been directed to the under- 
signed, has indicated a desire upon the part of 
the members of the law profession to know some- 
thing of the principles underlying the necessary 
calculations which form the basis for the imposi- 
tion of this form of taxation. To meet this want 
and to place before the profession generally an 
inexpensive book free from technical details and 
yet sufficiently comprehensive to enable one with 
practically no mathematical attainments to make 
the necessary calculations, may be briefly stated 
as the objects of the author. It is not intended 
as a text-book for actuaries or actuarial students, 
for they can find these subjects treated in a more 
thorough and scientific manner in the various text- 
books pertaining to their profession. , 

It is to the practicing lawyer, therefore, that I 
believe this book will prove both useful and at- 
tractive. I have spoken with a number of such 
men, and even those who enjoy large probate prac- 
tices have admitted their inability to verify the 
calculations of life estates and remainders which 
have been made for them by the designated State 
officers. In many cases these officers themselves 
admit their ignorance of the subject and are con- 

fiii] 



IV PREFACE. 

tent to give certificates which represent approxi- 
mations. 

The arrangement of the book is simple, and 
when once understood will enable one to calculate 
even the most coniplicated values quickly and with 
sufficient accuracy for all practical purposes. The 
advantage of this arrangement may be observed 
by comparing this with other books equally large 
and which give the possessor only the necessary 
tables for the calculations of dower and curtesy 
rights on one basis of mortality alone. Within 
these covers will be found the necessary instruc- 
tions and tables for the calculation of life estates, 
limited estates and vested remainders, contingent 
remainders, remainders that may be divested, 
dower, curtesy, inchoate dower, annuities of all 
kinds, etc., not only for one life, but for two, and 
in many cases three lives, on various bases, such 
as the American Experience Table of Mortality, 
Combined Experience, Carlisle Experience, and 
the Northampton Tables. 

The first part of the book consists of an exposi- 
tion of the principles underlying these calcula- 
tions, explaining the mortality tables, the method 
of adapting them to our uses and a simple expla- 
nation of the derivation of the necessary formulae. 
The second part of the book consists of a series of 
problems which explain in concrete form the ap- 
plication of the formulae derived in the first part 
of the book. These actual problems will enable 
the student to grasp the methods to be applied in 
a much shorter time than would a mere dealing 
with the propositions in an abstract manner. The 
numbers in brackets at the beginning of each 
problem refer to the numbers opposite the for- 



PKEFACE. V 

mulae in the first part of the book, and one is 
enabled thereby to immediately turn to the ex- 
planation relating to the derivation of the par- 
ticular formula with which he is working. The 
third part of the book consists of the tables 
which have been derived and which are to be used 
according to the requirements of the various State 
laws. In Michigan, New York, North Carolina, 
and Wisconsin, for instance, the American Ex- 
perience Table of Mortality is used. In Califor- 
nia, Iowa, Maine, and some other States the Ac- 
tuaries' or Combined Experience Table is pre- 
scribed, while in Pennsylvania, Tennessee, and 
Virginia the Carlisle Table is still used as a stand- 
ard. It will be noticed that a number of tables 
are given on the Northampton basis, which is still 
apparently used in many localities for the calcula- 
tion of dower rights. The fourth part of the book 
consists of a short discussion pertaining to the 
inheritance tax laws of the various States which 
will enable the reader to tell at a glance which 
standards are used in any particular State, so 
that he need not be in doubt as to the table of 
mortality which is to be used. It was deemed in- 
expedient to attempt to give a resume of the laws 
themselves, as they are constantly being changed 
with each session of the Legislatures, and each 
practicing attorney will unquestionably be fa- 
miliar with or able to ascertain what changes have 
been recently made. 

There is not much that may be termed original 
in the first part of the book, for these are well- 
established doctrines and theories which are fa- 
miliar to every actuary. Many of the tables, how- 
ever, in the third part have been derived and 



VI PEEFACE. 

computed especially for this book, and there is 
no doubt but that they will prove acceptable addi- 
tions to the tables now in use in many insurance 
offices. The graduated Carlisle Table, as set forth 
in volume XXII of the Journal of the Institute of 
Actuaries, has been used as a basis for those 
problems involving the Carlisle Table and more 
than one life. Similar problems on the American 
Experience Table have been worked by the Make- 
hamized Experience Table of Mortality, as set 
forth in a paper presented by Mr. Arthur Hunter 
to the Actuarial Society of America in May, 1902. 
Mr. Hunter's paper gave the values only on the 
3^ and 3^^ bases. This book contains the calcu- 
lations on a Sff basis. Some of the problems in- 
volvinjj two and three lives have been adapted 
from those given in Milne's book. Some of the 
tables involving the Combined and the Northamp- 
ton Tables of Mortality have been reproduced 
from some of the text-books in use in life offices, 
and from the tables published and distributed by 
the New York Insurance Department. 

I am indebted to Mr. Lee J. "Wolfe for his as- 
sistance in deriving most of the tables in Part III. 

S. H. Wolfe. 
35 Nassau Street, 

New Yoek, N. Y. 



TABLE OF CONTENTS. 



Pagb. 
Preface iii 

Chapter I. Tables of Mortality — An Early Roman Table — 
The Nortbampton and the Carlisle Tables — Observations 
of Edward Wigglesworth — Actuaries' or Combined Experi- 
ence Table — The American Experience Table — The Inter- 
est Factor 1 

Chapter II. Expectation of Life — The Method of Deriving 
It — Compound Interest — Rule for Calculating It for Any 
Period — Discount or Present Values — Rule for Finding 
Present Value of $1 Due at Various Periods 

Chapter III. Probability of Living -^ Present Value of 
Amount Payable if a Designated Life Survives a Given 
Period — Mortality Table Combined with Discount Value 
to Obtain the Present Value of a Life Estate Arithmetically. 10 

Chapter IV Commutation Columns — Method of Deriva- 
tion — The D Column — The N Column — Formula for Cal- 
culating the Present Value of a Life Estate from the Com- 
mutation Columns — Application of Formula — Derivation 
of Formulae for Temporary Annuity (use of an estate for a 
limited tei-m) and for Deferred Annuity — Combination of 
the F9regoing 14 

Chapter V. Inchoate Dower Rights — Joint Life Annuities — 
Derivation of Formula for Obtaining Same — Temporary 
Joint Life Annuities — Annuities Payable until the Extinc- 
tion of the Longer of Two Lives — Other Formulae Involv- 
ing Two Lives 20 

Chapter VI. Three Lives — Force of Mortality — Explana- 
tion of the Method of Applying This to Problems Involving 
More than One Life — The Equal Ages Method - Formulae 
for Various Annuity Problems Dealing with Three Lives. . 25 

Chapter VII. Vested Remainders — Proba'ality of Dying — 
Derivation of the C and the M Columns 33 

Chapter VIII. Joint Life Insurance — Remainders Which 
Vest upon the Death of Either of Two Designated Lives — 
Remainders Which Vest upon the Death of the Longer Lived 
of Two Designated Individuals — Contingent Remainders — 

Formula for Determining the Same 35 

[vii] 



VUl TABLE OF CONTENTS. 

Paqb. 
Chapter IX. Reasons for Calculating Life Estates and Re- 
mainders in the Same Manner that Premiums for Insurances 
and Annuities are Determined — Remainders Payable Im- 
mediately upon the Death of the Life Tenant — Curtate 
and Complete Annuities — Formulse for Ascertaining Pres- 
ent Value of Life Estates Payable in Installments during 
the Year 3S 

Explanation of Puoblems 45 

Pkoblems 47 

Index to Tablks 79 

Tables 81 

RfisHMfi OF Inheritance Tax Laws of the Various States. 259 

Key to Notation 293 

Index 297 



CHAPTER I. 



Tables of Mortality — An Early Roman Table 
— The Northampton and the Carlisle Tables — 
Observations of Edward Wigglesworth — Actu- 
aries' or Combined Experience Table — The 
American Experience Table ■ — The Interest 
Factor. 

The calculations of tlie values of life estates, 
vested remainders, contingent remainders, and 
other problems of a similar nature, the solution 
of wlaich is rendered necessary by the laws per- 
taining to collateral inheritance taxes, are pri- 
marily dependent upon the application of the 
probability of life and of death, and secondarily, 
upon the rate of interest which the statute as- 
sumes as a basis. We apply the doctrine of 
probabilities by means of a table of mortality 
compiled from actual sources of observation and 
graduated to eliminate any undue fluctuation due 
to the peculiar and abnormal conditions affecting 
the lives under observation. The first mortality 
table of which we have any record, is the one pre- 
pared by the eminent Roman jurist, the Praetorian 
PrsBfect Ulpianus, who, without doubt, was actu- 
ated by a desire to remedy the defects which 
existed in the crude method which had been em- 
ployed prior to his time in the valuation of 
annuities. It has been said that the first necessity 
for these judicial valuations was occasioned by 
the operations of the Falcidian law, by which a 
testator was prohibited from giving more than 

[1] 



ii INHERITANCE TAX CALCULATIONS. 

three-fourtlis of his property in legacies. The 
necessity, therefore, arose for valuing these lega- 
cies, which were in effect annuities either for life 
or for a shorter term. Numerous investigators 
have since compiled tahles of mortality based 
upon observations in their own localities, but they 
have more interest for the student of actuarial 
history than for those for whom this book is in- 
tended. There are two tables, however, which, 
although not employed by insurance companies at 
the present time to any great extent, must be re- 
ferred to as marking epochs in the history of 
annuity calculations. In 1771, Dr. Price pub- 
lished his famous work " Observations on Re- 
versionary Payments ; on Schemes for Providing 
Annuities for Widows, and for Persons in Old 
Age ; on the Method of Calculating the Values of 
Assurance on Lives, etc." Among the various 
tables included by the author in that book, was 
one showing the probability of life at Northamp- 
ton. This was the famous Northampton Table of 
Mortality employed for a great number of years 
by the actuaries of insurance companies and in- 
corporated in the statutes of a number of States as 
a basis for calculating dower rights. Forty- four 
years later Joshua Milne produced the Carlisle 
Table of Mortality. This table was long recog- 
nized as a standard, and, in fact, is still desig- 
nated in this country in the statutes of many of 
the States as a basis for dower and curtesy rights ; 
but in one State only (Tennessee) is it to-day 
specified as a basis for computation which must be 
used in fixing the values of annuities and life es- 
tates in collateral or inheritance tax' matters. 

In 1789, a professor of Harvard University, 
Edward Wigglesworth, published what is prob- 



INHEBITANCB TAX CALCULATIONS. A 

ably the first American observation on mortality. 
This table was based upon the early Bills of 
Mortality in the States of Massachusetts and New 
Hampshire, arfd it was afterwards adopted by the 
Supreme Court of the Commonwealth of Massa- 
chusetts for estimating the value of life estates. 
In 1838, a committee of English actuaries started 
the compilation of a mortality table which repre- 
sented the experience of seventeen life offices. 
The result of their investigations is known as the 
"Actuaries' or Combined Experience Table of 
Mortality," which for many years has been the 
standard for valuation purposes in a number of the 
States. It is specified at the present time as the 
basis for calculating annuities and reversionarj- 
interests in about half of the States whose stat- 
utes refer to any particular table of mortality, 
the balance using the "American Experience 
Table of Mortality." The latter is the work of 
Sheppard Homans; it appeared in 1868 and was 
based upon the experience of the Mutual Life In- 
surance Company of New York. This table was 
adopted by the Legislature of the State of New 
York as a standard for the valuations of the State. 
The second factor which enters into the value 
of life estates and remainders is the interest rate. 
This is a purely arbitrary quantity, varying with 
the dictates of the legislators of the various States 
and based approximately upon the earning power 
of money at the time of the enactment of the 
statute. The principal rates used in this country 
at the present time are 4^ and 5^, but in the tables 
which will be found in the following pages 6,^ 
has also been used in order to conform to the 
statutes of some of the States which still adhere 
to this high rate. 



CHAPTER II. 



Expectation of Life — The Method of Deriving it 

— Compound Interest — Rule for Calculating 
it for any Period — Discount or Present Values 

— Rule for Fitiding Present Value of $1 Due at 
Various Periods. 

The American Experience Table of Mortality, 
referred to in the previous pages, is as follows: 

Age. Ix 

10 100,000 

11 99,251 

12 98,505 

13 97,762 

14 97,022 

15 96,285 

16 95,550 

17 94,818 

18 94,089 

19 93,362 

20 92,637 

21 91,914 

22 91,192 

23 90,471 

24 89,751 

25 89,032 

26 88,314 

27 87,596 

28 86,878 

29 86,160 

30 85,441 

31 84,721 

32 84,000 

[4] 



dx 


Expec- 
tation. 


749 


48.72 


746 


48.09 


743 


47.45 


740 


46.80 


737 


46.16 


735 


45.51 


732 


44.85 


729 


44.19 


727 


43.53 


725 


42.87 


723 


42.20 


722 


41 . 53 


721 


40.85 


720 


40.17 


719 


39.49 


718 


38.81 


718 


38.12 


718 


37.43 


718 


36.73 


719 


36.03 


720 


35.33 


721 


34.63 


723 


33.92 



INHERITANCE TAX CALCULATIONS. 



Age. Ix 

33 83,277 

34. 82,551 

35 81,822 

36 81,090 

37 80,353 

38 79,611 

39 78,862 

40 78,106 

41 77,341 

42 76,567 

43 75,782 

44 -74,985 

45 74,173 

46 73,345 

47 72,497 

48 71,627 

49 70,731 

50 69,804 

51 68,842 

52 67,841 

53 66,797 

64 65,706 

55.. 64,563 

56 63,364 

57 62,104 

58 60,779 

69 59,385 

60 57,917 

61 56,371 

62.. 54,743 

63.. 53,030 

64 , 51,230 

65 49,341 

66 47,361 

67 *. 45,291 

68 43,133 

69.., 40,890 



da 


Ezpecv 
taUoa 


726 


33.21 


729 


32.50 


732 


31.78 


737 


31.07 


742 


30.35 


749 


29.63 


756 


28.90 


765 


28.18 


774 


27.45 


785 


26.72 


797 


25.99 


812 


25.27 


828 


24.54 


848 


23.81 


870 


23.08 


896 


22.35 


927 


21.63 


962 


20.91 


1,001 


20.20 


1,044 


19.49 


1,091 


18.79 


1,143 


18.09 


a,199 


17.40 


1,260 


16.72 


1,325 


16.05 


1,394 


15.39 


1,468 


14.74 


1,546 


14.10 


1,628 


13. 4T 


1,713 


12.8f> 


1,800 


12.26 


1,889 


11.67 


1,980 


11.10 


2,070 


10.54 


2,158 


10,00 


2,243 


9.47 


2,321 


8.97 



INHEEiTANCE TAX CALCULATIONS. 



ix 


dx 


Ezpeo- 
tationl 


38,569 


2,391 


8.48 


36,178 


2,448 


8.00 


33,730 


2,487 


7.55 


31,243 


2,505 


7.11 


28,738 


2,501 


6.68 


26,237 


2,476 


6.27 


23,761 


2,431 


5.88 


21,330 


2,369 


5.49 


18,961 


2,291 


5.11 


16,670 


2,196 


4.75 


14,474 


2,091 


4.39 


12;383 


1,964 


4.05 


10,419 


1,816 


3.71 


8,603 


1,648 


3.39 


6,955 


1,470 


3.08 


5,485 


1,292 


2.77 


4,193 


1,114 


2.47 


3,079 


933 


2.18 


2,146 


744 


1.91 


1,402 


555 


1.66 


847 


385 


1.42 


462 


246 


1.19 


216 


137 


.98 


79 


58 


.80 


21 


18 


.64 


3 


3 


.50 



Age. 

70. 
71. 

72. 
73. 
74. 
75. 
76. 
77. 
78. 
79. 
80. 
81. 
82. 
83. 
84. 
85. 
86. 
87. 
88. 
89. 
90. 
91. 
92. 
93. 
94. 
95. 



In tlie above table the first column shows the 
age of the life or lives under observation; the 
second column, known as the I column, indicates 
the number living at the various ages; the third 
column, known as the d column, shows the number 
dying at each age, and it will be apparent to the 
most casual observer that the value of d at any 
age is equal to the number living at that age, 
less the number living at the next higher age; 



INHEEITANCE TAX CALCULATIONS. 7 

the last column shows the expectation of life at 
the various ages, and this quantity may be defined 
as the average number of years which will be lived 
after a stated age. It is obtained by adding to- 
gether the number living at the various ages be- 
yond the one under observation, dividing this sum 
by the number living at the age of observation, and 
to the quotient adding six months. To find, for in- 
stance, the expectation of life at age 88, we would 
add together the numbers in the I column, begin- 
ning with 1,402 and continuing until the end of the 
table is reached. This sum, 3,030, we divide by the 
number living at age 88, viz. : 2,146, the quotient 
being 1.41; adding .5 of a year to this gives the 
expectation of life as 1.91 years. 

It is not an uncommon error for those attempt- 
ing to ascertain the value of a life estate to simply 
multiply the annual income by the number of 
years shown in the expectation of life column. 
This is absolutely incorrect, and the cause of the 
error and its magnitude will be appreciated when 
the manner of correctly computing annuities is 
explained. 

Interest. 

It has been explained that all annuity and re- 
versionary interest calculations are composed not 
only of the mortality element, but also of the in- 
terest element. It will be apparent that a given 
sum will produce a much larger life annuity if 
the calculations are made upon a 5^ interest 
earning basis than upon a 4^ assumption. It will 
be necessary, therefore, for the reader to familiar- 
ize himself with certain elementary facts concern- 
ing the accumulations of compound interest. 

If the amount of the principal be indicated by 1 



8 INHBKITANCB TAX CALCULATIONS. 

and the rate of interest by i the value at the end 
of a year's time will be 1 + *• At the end of the 
second year the accumulations will be represented 
by 

(1 + i) (l + i) which equals (l + i)\ 
At the end of the third year the accumulations 
will be 

(1 + iy (1 + i) which equals (1 + iy. 

Suppose we wish to determine the amount of 
$1 at 5^ compound interest at the end of each 
year for five years. From the above 
At the end of the 1st year 1 + .05 =$1.05 
At the end of the 2d year (1 + .05)^ = 1.1025 
At the end of the 3d year (1 + .05)" = 1.157625 
At the end of the 4th year (1 + .05)* = 1.21550& 
At the end of the 5th year (1 + .05)= = 1.276281 

This enables us to derive the general rule for 
compound interest, which is that, at the end of 
any given number of years the value of the prin- 
cipal may be determined if we add to it the rate 
of interest and raise this sum to the power equal 
to the nimiber of years. 

The determination of the present value of a sum 
due at some future period, may be described as 
the reciprocal operation to the foregoing. If 
l + i be taken as the representation of the amount 
of $1 at i rate of interest at the end of a year, 

then .. . will represent an amount which acciunu- 

lated at i rate of interest will exactly equal $1 
at the end of the year. In the same way it can be 

shown that .., , .. - will equal the present value of 
(1 + z)' 



INHERITANCE TAX CALCULATIONS. 9 

$1 due at the end of the second year, and .^ . ... 

(l + t)» 

will equal the present value of $1 at the end of 
the third year. The reader will notice that the 
denominators of these fractions are identical in 
form with the quantities representing the values 
of $1 accumulating at interest for the correspond- 
ing number of years in the preceding paragraph. 
If we wish to obtain, therefore, the present value 
of $1 at 5^ compound interest for the various 
periods up to five years, we would have 
Present value of $1 due in 1 year: 

1 I Qc ''=$•952381 
Present value of $1 due in 2 years : 

y-^ = $.907029 
Present value of $1 due in 3 years : 

1.157625 =$-863838 
Present value of $1 due in 4 years : 

j-2j5gQg = $. 822702 
Present value of $1 due in 5 years: 

07ki = *-^»5'26 

The rule, therefore, for determining the present 
value of any amount due at some future date, 
is to divide that amount by itself accumulated at 
the given rate of compound interest for the stated 
period. 

The two rules formulated above are essential 
to an understanding of the principles outlining 
the calculations of annuities and insurances. 



CHAPTER III. 



Probability of Living — Present Value of Amount 
Payable if a Designated Life Survives a Given 
Period — Mortality Table Combined with Dis- 
count Value to Obtain the Present Value of a 
Life Estate Arithmetically. 

We have already seen that we use the symbol I 
to indicate the number living, and in the follow- 
ing pages ho will indicate the number living at 
age 10, 111 the number living at age 11, etc. By 
referring to the American Experience Table of 
Mortality in Chapter II, it will be seen that 
ho = 100,000 
hi = 99,251 
hz = 98,505 
from which it is apparent that the probability of 
a person aged 10 surviving one year may be repre- 
sented by the fraction 

99,251 

100,000 

and the probability of a person aged 10 surviving 

two years will be represented by the fraction 

98,505 
100,000 
Disregarding for the moment the question of 
interest, it will be seen from the above that the 
value of $1 payable to a person aged 10, if he 
survives the year, plus the value of $1 payable to 
those aged 10 who survive the second year, may 
be represented by 

99,251 98,505 197,756 _ .. „ 



100,000 100,000 "100,000 

[10] 



INHEEITANCE TAX CALCULATIONS. 11 

In other words, if 100,000 pecjple aged 10 each 
paid $1.97 into a fund, it would enable the dis- 
tributor to pay $1 to each of the group wh^o lives 
one year, and $1 to each of the group who lives 
two years. In a similar manner the present value 
of $1 payable in a similar manner to the end of 
the mortality table limit, may be expressed 

[1] Jfll_ + ^^^^3_^^^^_ 

Ix ix -ix 

in which h represents the number living at any 
age, and of course U^i represents the number liv- 
ing at the next higher age. 

We must not, however, permit the fact to escape 
us that a calculation of this kind is incomplete 
without the interest element. We must, there- 
fore, discount the values of the probabilities ex- 
pressed in the foregoing analysis by the rate of 
interest which we assume will be earned. Sup- 
pose that we should desire to calculate according 
to the American Experience Table of Mortality, 
with 5^ interest, the value of a life estate of a 
beneficiary aged 90, the annual income from the 
testator's estate being $1. So advanced an age 
is assumed in order that we may complete our 
calculations to the tabular limit without undue 
repetition. According to the Table of Mortality, 
we find: 

At age 90 there will be 847 living. 
At age 91 there will be 462 living. 
At age 92 there will be 216 living. 
At age 93 there will be 79 living. 
At age 94 there will be 21 living. 
At age 95 there will be 3 living. 

By referring to the preceding chapter on the 



12 ' INHEEITANCE TAX CALCULATIONS. 

present values of $1 due at stated periods, we 
find that the 

Present value at 5^ of $1 at end of 1 year is 
. 952381 

Present value at 5^ of $1 at end of 2 years is 
.907029 

Present value at 5^ of $1 at end of 3 years is 
.863838 

Present value at 5^ of $1 at end of 4 years is 
.822702 ■ 

Present value at 5^ of $1 at end of 5 years is 
.783526 

Bearing in mind the above data it will be ap- 
parent that the present value, of a payment of 
$1 to a person aged 90 surviving one year will be 

462 X .952381 

847 

In the same way the present value of $1 payable 
to a person aged 90, if he survives the second 
year, will be represented by 

216 X .907029 

847 

The present value of the third payment will be 

79 X .863838 

847 

The present value of the fourth payment will be 

21 X .822702 

847 

and the present value of the fifth payment will be 

3 X .783526 

847 

The sum of the series, therefore, which repre- 



INHEEITANCE TAX CALCULATIONS. 13 

sents the value of the life estate of this beneficiary 
is expressed 

(468X .952881) + (816 X -907089) + (79 X .863838) + (81 >< .882702) + (3 X .783528) 

847 

[2] 

Performing these arithmetical calculations we 
obtain as a result .8545 which means that accord- 
ing to the American Experience Table of Mortal- 
ity and 5^ interest, the value of a life estate of 
$1 per annum of a person aged 90 is $.8545. 

This analytical method, while giving absolutely 
correct results, is cumbersome and from a prac- 
tical standpoint impossible of use when it is 
desired to obtain the value of life estates of bene*- 
fieiaries of yo'unger ages. W.e are enabled, how- 
ever, by the employment of an arrangement known 
as the Commutation Columns to materially 
shorten the calculation and obtain the desired re- 
sult by one operation. The method of obtaining 
these columns will be explained in the next 
chapter. 



CHAPTER IV. 



Commutation Columns — Method of Derivation 
— The D Column — The N Column — Formula 
for Calculating the Present Value of a Life 
Estate from the Commutation Cohimns — Ap- 
plication of Formula — Derivation of Formulce 
for Temporary Annuity (use of an estate for 
a limited term) and for Deferred Annuity — 
Combination of the Foregoing. 

The names of Dale, Morgan, Barrett, and Grif- 
fith Davies are all connected with the earlier work 
of the development of the Con^jmutation Columns, 
but to Professor John Nicholas Tetens, of the 
University of Kiel, belongs the credit of publish- 
ing what is probably the most lucid description 
of these aids to actuarial calculations. In 1785 
he introduced the method of multiplying the 
numerator and denominator of the fractions 
(shown in the preceding chapter) representing the 
present value of a unit to be paid to a person 
aged X at the end of the various years, by the dis- 
counted value of $1 at a given rate of interest 
raised to a power equal to the age of the life under 
observation. Since he multiplied both the numer- 
ator and denominator of the fraction, it did not, 
of course, affect its value. The utility of this 
method will, however, be observed after the proc- 
ess of calculating these columns has been ex- 
plained. 

[U] 



INHEEITANCE TAX CALCULATIONS. 15 

Referring to Formula [1] in the preceding 
chapter, which is 

w+i ta;+; lix+3 
—J h -^ h —, h etc. 

t/X IfX vx 

let us put it in the more condensed form of 

tx+t ~r~ vx+z r 'ir+3 ~r etc. 

tx 

It will be recalled that the value of a life es- 
tate depends not only upon the mortality element, 
but also upon the rate of interest which the stat- 
ute assumes. We must, therefore, introduce the 
discounted value of $1 as shown in Formula [2]. 
Representing this discounted value by the symbol 
V we have 

t/W VX t/X 

which gives 

ix 

which the reader will recognize as identical in 
form with Formula [2]. 

Multiplying the numerator and denominator of 
a fraction by the same quantity does not change 
its value. Let us multiply the numerator and 
denominator of the fraction just obtained by v'' 
and we have for a result 

( L.i) {v'*') + {lx.,) {v^'')+{lx.,) {v-'')+ etc . 

IxV" 

Representing 

Ix V by Dx 
Ix,, v^'' by D^,i 
U^ V*" by D^+2 
Ix,, v^'' by D^,3 



16 INHERITANCE TAX CALCULATIONS. 

we have 

P^ti + D^t2 + D»^-3 + etc. 

Da, 

And if we represent the value of the series 

Da,.i + D^+2 + D;5^3 + etc. by N^^+i 
we have as the value of the foregoing fraction 
[3] . N^^ 

If we, therefore, once work out the values of 
N and D we will be enabled to immediately cal- 
culate the value of an estate for life, an estate 
for a limited term of years, an estate the value 
of which will not be enjoyed by the beneficiaries 
until a certain number of years have elapsed, 
and the various problems which arise in matters 
connected with annuities. 

The values of the N and D columns have been 
worked out and will be found under various tables 
in the second part of this book. To illustrate the 
manner of applying the formula just arrived at, 
let us obtain the value of a life estate of a bene- 
ficiary aged 90, according to the American Ex- 
perience Table of Mortality and 5^ interest. 

By referring to Table XXX we see that 
N,,^ 8.96550843 and 
D„„ = 10.49171277 
Dividing the first by the second we obtain as a 
result .8545 which will be recognized as the same 
answer that was obtained by the laborious arith- 
methical computations performed in the solution 
of Formula [2]. 

It must be borne in mind that the Commutation 
Columns for each table of mortality and each 



INHERITANCE TAX CALCULATIONS. 17 

rate of interest are different. To determine the 
value, therefore, of any life estate, divide the 
figure found in the N column opposite the age one 
year higher than the beneficiary's, by the figure 
found in the D column opposite the age of the 
beneficiary, being careful to use the Commutation 
Columns of the correct table of mortality and rate 
of interest. 

To determine the value of a temporary annuity 
or an estate for a limited number of years, is a 
comparatively simple matter once the Commuta- 
tion Columns have been worked out. Instead of 
carrying the calculations to age 95, which is the' 
limit of the American Experience Table of Mor- 
tality, we stop at the end of the number of years 
for which the beneficiary is to enjoy the estate. 
Suppose, for instance, we wish to determine the 
value of a temporary annuity for two years. We 
may represent this by 

which the reader will recognize as the beginning 
of the same process which resulted in Formula 
[3]. ' Using the same substituted values, we have 
for the value of this temporary annuity 

Remembering that Na, represents the value of 
the entire series from age x to the end of the 
table, it will be apparent that the numerator in 
this fraction becomes 

so that the fraction may be expressed as 
3 



18 INHEEITANCE TAX CALCULATIONS. 

from which we derive the rule that the value of 
a temporary annuity may be found by subtract- 
ing from the figure in the N column opposite the 
age one year greater than the beneficiary's, the 
figure in the N column opposite the age repre- 
sented by the beneficiary's age increased by one 
more year than is contained in the term for which 
the estate is to be enjoyed, this remainder being 
divided by the figure in the D column opposite the 
age of the beneficiary. This rule expressed alge- 
braically is 
[4] N.,1 — N. 



' •'•+1+1 



in which the n is the number of annual payments 
which are to be enjoyed by the beneficiary, the 
first of which is to be made one year after the 
testator's death. 

A deferred annuity may be defined as one which 
begins at some definite date in the future and 
continues from that time until the end of the life 
of the beneficiary. 

From the foregoing explanation it will be ap- 
parent that this form of annuity may be repre- 
sented by the fraction 

[5] N.,n 

in which n represents the number of years for 
which the first payment is to be deferred. A life 
estate, for instance, the enjoyment of which is 
not to begin until five years after the death of the 
testator, would in the case of a beneficiary 40 
years old have for its value 



INHEBITANCK TAX CALCULATIONS. 19 

The rule in this case is so obvious that it is 
unnecessary to formulate one. 

It is not an uncommon thing to be called upon 
to calculate the value of an estate, the terms of 
which are a combination of Formulaj [4] and 
[5]. Such a case would be represented by a con- 
dition of affairs whereby the beneficiary was to 
enjoy the estate only after a certain number of 
years had elapsed and then only for a limited 
period. To use a concrete illustration, if we were 
required to ascertain the value of an annuity 
which a benefiiciary age 40 at the time of the 
death of the testator was to enjoy for a period 
commencing ten years after the testator's death 
and to continue for twenty years and no longer, 
the formula would be 

40+10 ^"40+10+20 ^^ SO ■'^ 70 

^0 ~ D40 

the general formula for a deferred temporary 
annuity being 

[6] N^^n — N^ 



* x+fi-^fn 



D^ 



in which the symbol n represents the number of 
years for which the temporary annuity is defer- 
red, and the symbol m represents the number of 
years for which the annuity is to continue. 



CHAPTER V. 



Inchoate Dower Rights — Joint Life Annuities — 
Derivation of Formula for Obtaining Same- — 
Temporary Joint Life Annuities — Annuities 
Payable Until the Extinction of the Longer of ^ 
Two Lives — Other Formulce Involving Two 
Lives. 

In dealing with the various problems which 
arise in connection with inchoate dower rights, 
estates, the enjoyment of which is dependent upon 
the survivorship of a designated life, and other 
matters of a similar nature, we emplc^y joint life 
annuities. A joint life annuity is one which is 
payable as long as all the parties continue to 
live, and, therefore, ceases as soon as one of the 
lives makes its exit. A joint annuity on the lives 
of X and y would be payable as long as they both 
lived, but upon the death of either, the annuity 
payments would cease. The manner in which this 
form is found useful in calculating inchoate dower 
rights, is best illustrated by analyzing the condi- 
tions which exist in a case of that kind, y, the 
wife of X, is entitled as a dower right to the annual 
income which arises from one-third of the estate 
of X upon his decease. The value of such a life 
estate would easily be ascertainable from the for- 
mula outlined in the preceding chapter, were it 
not for the fact that her income does not start 
until the death of x. We must, therefore, decrease 
the value of the life estate of y by an amount which 
represents the joint existence of x and y. This 

[20] 



INHERITANCE TAX CALCULATIONS. 21 

latter factor is the joint annuity, and the rule for 
determining an inchoate dower right is, therefore, 
to deduct from the value of the annuity on the 
wife's life (based on an amount equal to one- 
third of the income of the husband's estate) a 
sum equal to the joint life annuity of the husband 
and the wife for the same amount. The manner 
of obtaining joint life values is as follows: 

The probability of two lives surviving a given 
period is the product of the separate probabilities 
that each will survive the same period. If, as 
was pointed out in Chapter II, the probability of 

X surviving one year be represented by -^p- and 

the probability of y surviving the same period be 

represented by -yi the probability of the two lives 

both surviving one year will be represented by 
the fraction 

( l^+i ) ( h-n ) 
Ix iy 

It will be unnecessary to go through the various 
steps similar to those employed in the derivation 
of formulae for single lives, for the reader with- 
out doubt recognizes that the value of a joint life 
annuity payable during the existence of x and y, 
will be 

(Ix^t) (ly^i) V + (L42) (W) f ' + (h+s) {h+3) v^ + etc. 

Ix iy 

Making similar substitutions, we obtain for the 
final form of the expression 

17] N.,,.„,, 

It will be apparent likewise that this is a gen- 
eral formula which holds true for any number of 



22 INHERITANCE TAX CALCULATIONS. 

lives, and the value of a joint life annuity on three 
lives would be expressed by 



This formula holds true for all ages of x and 
y, and the great number of combinations which 
result from giving different values to x and y is 
responsible for the extensive tables which have 
been published to enable observers to obtain 
values on joint lives. It is the intention of the 
author, however, to obviate this objection as much 
as possible by employing the Equal Ages method 
which he has applied to many of the tables of 
joint life annuities and joint single premiums to 
be found in the second part of this book. For this 
purpose he has used the graduated Carlisle Table 
and the American Experience Table of Mortality 
as graduated by Mr. Arthur Hunter in accordance 
with the Makeham formula used by King and 
Hardy. By referring to the tables showing the 
Force of Mortality, the reader will find the neces- 
sary figures to enable him to obtain the equal 
ages which are the equivalent of any pair of dif- 
ferent ages. By then referring to tables which 
give the joint life annuity values for two equal 
ages, we obtain the exact value. The way to use 
the Force of Mortality Tables is explained in 
Chapter VI and in the problems in the second 
part of the book. 

In the same manner a temporary joint annuity 
on two lives to run n years is represented by 



INHERITANCE TAX CALCULATIONS. 23 

and an annuity deferred for n years on two joint 
lives may be represented by 



There are some forms of joint life estates, for 
the solution of which we require a slightly differ- 
ent formula. We may, for instance, desire to 
know the value of an annuity of $1 per annum 
payable to the survivor of two specified lives. An- 
other way of expressing this problem would be 
to require an annuity of $1 per annum on two 
lives X and y which is to continue until both have 
died. It will be evident to the reader that if we 
add the two single life annuities together and sub- 
tract from this sum the value of a joint life an- 
nuity, we shall have the required solution; hence 

LO J dw ~j~ Oiy dxy 

the symbol a being employed in the above formula 
for the word " annuity " and as a substitute for 
the more lengthy form heretofore employed. This 
formula will, of course, be recognized in its longer 
form as 

iJx L^y *-^i'y 

Another combination which may sometimes be 
required is the obtainment of the value of an 
annuity on the life of y to commence after the 
death of x. By the same line of reasoning, this 
value will be found to equal the single annuity on 
y's life minus the joint annuity on the lives of 
X and y, or 
[9] ay — axy 

That this will meet the conditions the reader 
will be able to observe, for as long as both x and y 



24 INHEEITANCE TAX CALCULATIONS. 

live the value of the joint life annuity is equal to 
the annuity on y's life, and the result is 0. Should 
X die before y the value of axv becomes and y 
enters upon his annuity. Should y die before x 
both values reduce to 0, so that the conditions of 
the problem are met in every particular. It is this 
formula which is used in calculating the present 
value of inchoate dower rights. 

If we should desire to calculate the value of the 
interest of x in an annuity which is to be equally 
divided between x and y as long as they both live, 
and when one of them dies the survivor is to en- 
joy the entire annuity as long as he lives, we 
would be able to obtain the result by subtracting 
from the annuity on the life of x one-half of the 
joint life annuity. This expressed as a formula 
would be 
[10] Ux — iaxy 

In the same way the value of y's interest in the 
foregoing case would be 

Ojy ^dxy 

If we desire to find the value of an annuity 
which is to be payable to the longer lived of two 
lives, X and y, the annuity payments to commence 
upon the death of the first one, we would be en- 
abled to do so by applying the formula 

[II] ax-\-ay — 2axv 

It will be observed that this is made up of two 
factors : First, the value of an annuity on x's life 
minus the joint life annuity on the lives of x and 
y, and second, the value of an annuity on the life 
of y minus the joint life annuity, i. e., 

O* Oixy + Oy Uxy = ttx -\- Cly iUxy 



CHAPTER VI. 



Three Lives — Force of Mortality — Explanation 
of the Method of Applying this to Problems In- 
volving More Than One Life — The Equal Ages 
Method — Formula for Various Annuity Prob- 
lems Dealing with Three Lives. 

The problems heretofore given have dealt only 
with the contingencies dependent upon the exist- 
ence or failure of one or two lives. In practice 
the necessity arises for securing values on life 
estates and remainders where three or more lives 
enter into the computations. The same theories 
hold good for three lives as for two lives, but the 
practical application of the formulse intended for 
the greater number of lives is naturally more 
difficult. This may be realized by a comparison of 
the results obtained by calculating the probability, 
first, that a person aged 30 will survive one year; 
second, that two persons aged 30 shall both sur- 
vive one year, and third, that three persons aged 
30 shall all survive one year. Using the American 
Experience Table of Mortality, 



U, _ 84721 



^9916 



L 85441 

4701 

= .9832 



?«„.»« _ 84721 X 84721 



hy 85441 X 85441 

[12] ?».,.,.i...x ^ 84721 X 84721 X 84721 ^ 
L^ 85441 X 85441 X 85441 " 

It will be apparent, therefore, that the calcula- 
tion of joint life values on three or more lives 
by preparing tables for every possible combina- 

[25] 



26 INHERITANCE TAX CALCULATIONS. 

tion of ages, would be a stupendous undertaking, 
the results of which would be beyond the reach 
of those for whom these calculations are intended. 
In Chapter V, a method was pointed out 
whereby two lives were reduced to the equivalent 
equal ages, we being, therefore, enabled to obtain 
all of our values by calculating one set of values 
only. The same method may be applied to prob- 
lems involving three or more lives. This is done 
by means of a table known as the " Force of 
Mortality." If we add together the force of 
mortality of the ages under observation and divide 
by 3, we shall have a practically correct repre- 
sentation of the force of mortality of the equiva- 
lent equal ages. To illustrate: If we desire to 
know the equivalent equal ages of three lives 
according to the Makehamized American Experi- 
ence, aged 20, 25, and 30, we find by reference to 
the table just mentioned (see Table III in the 
third part of this book) that the force of mortality 
of each age is as follows : 

Age 20 00786 

Age 25 00804 

Age 30 00835 

.02425 
Dividing this by 3 we find that the force of mortal- 
ity of the equivalent equal ages which we want 
is .00808. By examining the same table we find 
that .00808 is situated somewhere between ages 
25 and 26. To ascertain its exact point we pro- 
ceed as follows: 

Force of Mortality age 26 = .00809 
Force of Mortality age 25 = .00804 

Difference = .00005 



INHERITANCE TAX CALCT7LATTONS. 27 

The difference between the desired equal ages 
and age 25 is .00004 (found by subtracting .00804 
from .00808). The point we desire is, therefore, 

nonfl'i ^^ '^ beyond age 25. The equivalent, there- 
fore, of three lives aged 20, 25, and 30, are three 
lives each aged 25.8 years. Once having found 
the equivalent equal ages, we proceed to calculate 
as heretofore, being careful to use only those 
tables applicable to three lives. 

The method having been described of obtain- 
ing calculations for three or more lives, we are 
prepared to start to solve the various problems 
which arise in connection therewith. 

In the preceding chapter the method of obtain- 
ing the value of an annuity on two lives, x and y, 
which is continued until both have died, was ex- 
plained. (Formula [8].) If instead of two lives 
we desire to obtain the value of an annuity on 
the longest of three lives, the result will equal 

{ -lo J Q/x ~T~ ^1/ ~F ^2 Oixp (Ixs Clys ~T~ O/xy^ 

To test the correctness of this formula, assume 
that the annuity is for $1 per annum. As long 
as X, y, and z are alive it will be seen that accord- 
ing to the formula the net result will be $1. If 
X then dies ax, axy, and axyz disappear, and the ex- 
pression then takes the form of 

Ojy ~\~ Oiz - — Gys 

which will be recognized as identical with 
Formula [8]. 

Another problem which may arise is the deter- 
mination of the present value of an annuity to 
commence at the present time and end with the 
next to the last death of three lives, i. e., to con- 



28 INHERITANCE TAX CALCULATIONS. 

tinue as long as two of the three lives are in 
existence. This expression takes the form of 

[14] ax» -\- Oyz -\- ttxz 2axyz 

Testing this as we did in the previous case, we 
find that as long as x, y, and z are all alive the 
value of the formula reduces to 1; but as soon 
as any one life, x, for instance, disappears, the 
first, third, and fourth terms of the expression dis- 
appear, leaving 

dyz 

which will be at once recognized as the expression 
for a joint life annuity, viz., one that continues 
until the death of one of the lives, which, it will 
be observed, meets the requirements of the prob- 
lem exactly. 

If we should be required to determine the value 
of an annuity on the life of x to commence as soon 
as 2/ or s dies, we should be able to do so by ap- 
plying the formula 

[_J.0J Q/x Cixyx 

for as long as the three lives are in existence 
the value of the expression will be 0, but as soon 
as 2/ or 2! dies the annuity on x would start. If x 
should die before y or z, the entire expression 
would be reduced to 0. If, however, the problem 
takes the form of determining the value of the 
annuity on the life of x after the death oi both y 
and s, we could obtain it by solving the expression 

[16] ttx axy ttxz -\- ttxyz 

A modification of the foregoing would be to 
determine the value of an annuity on the joint 
lives of y and z to commence after the death of x. 
This it will be readily seen is 

[17] Oyi Oxyt 



INHEBITANCE TAX CALCULATIONS. 29 

Another form, the solution of which may be 
found useful in practice, is the value of an annuity 
to be paid to the survivor of x and y after the third 
party, z, dies. This expression is 

|_XoJ Qtx ~T~ ^y ^i^J/ ^xfi (^yz \ Cixyz 

Another form, the solution of which may at 
times be required, is the determination of the 
value of an annuity which is not to commence 
until one of three designated lives expires, and is 
to continue only until the death of one of the re- 
maining two. This would be 

l_J-yj dxy ~F Qjxz ~\~ Ojyz ~ — oQixyz 

In one of the problems outlined in the preced- 
ing chapter, we have the method to be followed in 
obtaining the value of the interest of either of 
the two lives in an annuity which was to be divided 
equally between them during the joint survivor- 
ship and to go to the survivor upon the first 
death. We may in a similar manner determine 
the value of an annuity to be divided equally be- 
tween the survivors of three lives, the expression 
taking the form of 

Value of X 's interest = ax — ^axy — loxz -f laxyz 
Value of ?/'s interest = ay — ^axy — layz + ^axyz 
Value of s's interest = a« — ^axz — ^Oyz + laxyz 

To prove the correctness of the foregoing, it 
is only necessary for us to add the interests of 
X, y, and z together and observe whether we obtain 
by this sum the whole value of the annuity. Per- 
forming the addition the result is 

O/x ~j~ dy ~X' OjZ Qixy dyz dxz ~\~ Ctxfz 

which will be recognized as Formula [13] which 
represents the value of an annuity on the longest 
of three lives, the exact conditions of this problem. 



30 INHERITANCE TAX CALCULATIONS. 

Joshua Milne, who has already been referred to 
as the producer of the Carlisle Table of Mortality, 
gives a number of interesting problems on the 
partition of annuities, some of them in this chap- 
ter being taken from his book. 

Two lives, X and y, are the possessors of an 
annuity payable to the one who survives the 
longer. Should, however, a third party, z, be alive 
at the death of either x or y, he is to share in the 
annuity which becomes payable to the survivor. 
The value of the interests of x and y can, of course, 
be determined from the formulae already given. 
The value of z's interest, however, will be 

[20] laxe + ^ttyz axyz 

If it should be desired to calculate the value of 
x's interest in an annuity on the last two survivors 
of three lives which is to be divided equally among 
them during their joint existence, and after the 
death of the first one is to be divided equally be- 
tween the two remaining ones until one of them 
shall die, we would be enabled to obtain the value 
of any life's interest, such as x, as follows: 

[21] Value of ic's interest = \dxv + laxz — %axvi 

Another problem which Milne gives is the cal- 
culation of an annuity which after the decease of 
x is to be divided equally between two other lives, 
y and z, as long as they shall both live ; after the 
death of either y or z the annuity is then to be 
paid to the survivor as long as he shall live, y's 
interest in this case would be 

[22] Oy axy ^ttyz "h ^ttxyz 

Another modification of this would be to deter- 
mine x's interest in an annuity on the last survivor 
of three lives which is to be divided equally be- 



INHEBITANCB TAX CALCULATIONS. 31 

tween two of them, x and y, during their joint ex- 
istence; after the death of either one of them it 
is to be divided then equally between z, if then 
living, and the survivor during their joint exist- 
ence; and if there is but one survivor, he shall 
receive the whole of the remaining annuity. In 
this case x's interest equals 

These combinations which have been given 
afford the reader the opportunity of analyzing the 
conditions of each problem. Actual arithmetical 
Bolutions, i. e., the application of these formulEe 
to actual cases, will be found in the second part 
of the book preceding the tables. 



CHAPTER VII. 



Vested Remainders — Probability of Dying — 
Derivation of the C and the M Columns. 

The present value of a vested remainder from 
the actuarial standpoint may be defined as that 
amount which upon the assumed mortality and 
interest bases will equal the testator's estate at 
the time of the death of the life tenant. 

In Chapter III, we have learned that the prob- 
ability of a person age 10 surviving one year 
is represented by the fraction 

ho 100,000 -^^^ 

By referring to the American Experience Table 
of Mortality given in Chapter II, we see that of 
the 100,000 people living at age 10, there will die 
during the year 749. The probability of death, 
therefore, will be 

749 
LZH_= 00749 

100.000 -^^'^^ 

Since the probability of a thing happening plus 
the probability of it not happening, must always 
equal unity, it will be observed that the probability 
of a person age 10 living one year, or .99251, when 
added to the probability of the same person dying 
during the year, or .00749, equals unity. 

Indicating the number of persons at age x who 
will die during the year by the symbol dx we have 

j^ = probability of death during the first year 

[32] 



INHEEITANCE TAX CALCXJLATIONS. 33 

-j^ = probability of death during the second year 

-^ - probability of death during the third year. 

The probability, therefore, that a person aged x 
will die within three years is represented by the 
sum of these separate probabilities, or 

dx I Ux+i Ux+2 dx ~r dx+i -f" Ml+2 

vx ix ix ix 

In order to obtain the monetary value, how- 
ever, we must remember that we must introduce 
the interest factor. We must, therefore, discount 
the values of the probabilities of death shown 
in the foregorug expression by the rate of interest 
which we assume will be earned. Using the same 
symbol as in Chapter IV for this discounted value, 
V, we would have as the representation of the 
probabilities of the heirs of a person age x receiv- 
ing $1 if that person should die within three years. 

(dx) (v) + {dx,,) iv') + {dx.,) jv') 

Ix 

and in the same way the value of the probability 
of the heirs of a person aged x receiving $1 upon 
the death of that person, would be represented 
by the same expression carried out to the limits 
of the mortality table, or ' 

{dx){v) + (dx,^) iv') + {dx.,){vn + {dx.s) {v*)+etc. 

Ix 

Multiplying the numerator and denominator 
of this fraction by v' which does not change its 
value, we have 

(& ) (i>H-') -I- (<fcH-i) («^') + (d^i) (v>+^ + (d=>i-3) (v=^) + etc 
3 



34 INHERITANCE TAX CALCULATIONS. 

It has already been pointed out that calcula- 
tions of this nature can be greatly shortened by 
means of the arrangement known as the Commu- 
tation Columns. By reference to Chapter IV it 
will be seen that we represented L v'' by D^, and 
L+i v"*^ by D^^i. In the same manner let us rep- 
resent dxv"*^ by Cx and d^^iV'^''- by Ca,+i. Sub- 
stituting these values in the fraction we have just 
derived, we have 

V^x "T ^x^\ "P ^a:-:.2 ~r ^^^+3 "T" CtC. 

We have already represented Da; -f Dx^^ -\- Da^., 
+ the rest of the series by the symbol N, and in the 
same manner we will represent the values of the 
series C^ -f- Cx^i + Ca^+a to the tabular limit by the 
symbol M^-. The fraction stated above, therefore, 
reduces itself to the form 

[24] M. 

D, 

The values of M^, and D^, have already been 
worked out for all ages, so that in order to obtain 
the value of $1 payable when a person aged x 
dies, it will simply be necessary to divide the fig- 
ure found opposite that age in the M column by 
the figure found opposite the same age in the D 
column. 



CHAPTER VIII. 



Joint Life Insurance — Remainders which Vest 
upon the Death of Either of Two Designated 
Lives — Remainders which Vest upon the Death 
of the Longer Lived of Two Designated Indi- 
viduals — Contingent Remainders — Formula 
for Determining the Same. 

The reader by this time is familiar enough with 
the general subject to appreciate that the joint 
life insurance on two lives, x and y, payable at 
the death of the first life, will be represented by 

[25] }ILy 

It must be borne in mind that a difference ex- 
ists between a joint life annuity and a joint life 
insurance. In the former the payments are made 
during the joint existence of the two lives, while in 
the latter case the amount does not become pay- 
able until one of the lives has ceased. 

The simplest way of dealing with joint lives is 
by the Equal Ages method which has already been 
explained. To recapitulate: Add together the 
force of mortality (being careful to use the 
proper mortality experience) as shown in Table 
III, divide by the number of lives and ascertain 
the equivalent age at which this new force of 
mortality will be found. This age will represent 
the equal ages, and the final result may be ob- 
tained either directly from the single premiums 
for joint lives, which have already been worked 
out, or by direct reference to the M^ and D 
commutation columns. 

[35] 



jsa- 



36 INHEEITANCE TAX CALCULATIONS. 

There is not as great a variety of problems in- 
volving values of remainders as there are involv- 
ing the values of life, future, and.]imited estates. 
It may sometimes be necessary, libwever, to de- 
termine the value of a remainder (or insurance) 
payable not upon the death of the first of a desig- 
nated pair of lives, but payable upon the death of 
the longer lived of the two. In this case it will be 
apparent that the value desired will be the sum 
of the single premiums on each of the individual 
lives less the premium for their joint life insur- 
ance. The expression, therefore, becomes 

[26] M^ M„ _ M^„ 

By referring to the chapters on annuities, it 
will be noted that we used the symbol a to desig- 
nate the word " annuity." In the same way let 
us use the symbol A to designate the single pre- 
mium or the value of the remainder, in which 
case the foregoing expression takes the form of 

Mr. Arthur Hunter has pointed out an excellent 
way of using his Makehamized American Experi- 
ence Table in the solution of many of the com- 
plicated problems which arise in connection with 
contingent insurances. Since all of the tables of 
mortality have not been graduated by the Make- 
ham method, it is, therefore, not possible to apply 
the Equal Ages method in all cases. There will 
be found in the back of the book tables derived 
from the graduated Carlisle and American tables. 
An illustration of the adaptability of these modi- 
fications to contingent insurances may be observed 
from the following problem. 



INHERITANCE TAX CALCULATIONS. 37 

If, for instance, we should require the premium 
to insure $1 receivable at the end of the year in 
which X dies, provided another life, y, be then liv- 
ing, we should be able to obtain it by means of 
the formula shown below. It may be mentioned 
in passing that it is this problem which is in- 
volved in the determination of the value of many 
contingent estates where, for instance, a testator 
gives his widow his estate for life with the re- 
mainder over to a daughter, if she be living at 
the death of her mother, or in the event of her 
prior death the remainder to pass to the child of 
the daughter (the grandchild of the testator). 
This form is frequently termed " The Insurance 
of X against y. ' ' The value of the contingent re- 
mainder of the testator's daughter in the above 
case is the premium necessary to secure the value 
of the estate (as appraised at time of the tes- 
tator's death) when the widow {x) dies, pro- 
viding the daughter {y) is living at that time. 
The formula by which a value of this kind may 
be determined is 

[27] v^ \}>-x (a^» + i) + i (a^-i.!/ — az^x.v) ] 

The practical application of a problem of this 
kind will be found in the second part of the book. 

The problems involving three lives are not met 
with so frequently in the determination of re- 
mainders for inheritance tax purposes. The same 
principles which are applicable to three lives in 
calculating the life estates are, when modified, 
used in obtaining formulae for contingent remain- 
ders. The author does not deem it necessary or 
advisable, however, to take up those problems at 
this time. 



CHAPTER IX. 



Reasons for Calculating Life Estates and Re- 
mainders in the Same Manner that Premiums 
for Insurances and Annuities are Determined 
— Remainders Payable Immediately Upon the 
Death of the Life Tenant — Curtate and Com- 
plete Annuities — Formulce for Ascertaining 
Present Value of Life Estates Payable in In- 
stallments during the Year. 

In the preceding chapters it will be noticed that 
the life estates have been calculated as though 
they were annuities issued by insurance com- 
panies, and remainders have been calculated as 
though they were insurances granted by the same 
class of corporations. This method was adopted 
purposely, as such was unquestionably the intent 
of the legislators when they enacted the Inherit- 
ance Tax Laws. In some of the States the di- 
rections are specific. In Wisconsin, for instance, 
it is provided that " The value of every future 
or limited estate, income, interest, or annuity de- 
pendent upon any life or lives in being, shall be 
determined by the rule, method, and standard of 
mortality and value employed by the commis- 
sioner of insurance in ascertaining the value of 
policies of life insurance and annuities for the 
determination of liabilities of life insurance com- 
panies except that the rate of interest for making 
such computation shall be at the rate of five per 
centum per annum." In New York " The super- 
intendent of insurance shall, on application of 

[38] 



INHERITANCE TAX CALCULATIONS. 39 

any surrogate, determine the value of any such 
future contingent estate, income or interest 
therein, limited, dependent, contingent or deter- 
minable upon the life or lives of the persons in 
being, upon the facts contained in any such ap- 
praiser's report, and certify the same to the sur- 
rogate, and his certificate shall be conclusive evi- 
dence that the method of computation adopted 
therein is correct." The Superintendent of In- 
surance in New York has not published any rules, 
standards of mortality, or methods indicating the 
ones employed by him in making these compu- 
tations for the surrogates. If we take the value 
of a life estate and a vested remainder, as set 
forth in any certificate issued by this officer, and 
compare the values given therein with those ob- 
tained by means of the formulae in the preceding 
chapters, it will be seen that the results are iden- 
tical. It will likewise be noted that the value of 
the vested remainder plus the present value of 
the life estate will not exactly equal the appraised 
value of the testator's property at the time of his 
death. It is but natural that the reader should 
desire an explanation of what may appear to him 
an error. The explanation, however, is compara- 
tively simple and will be readily understood from 
the following: 

The basis upon which life insurance premiums 
are calculated contemplates the payment of the 
premium in advance at each anniversary of the 
policy and the payment of the death loss at the 
end of the policy year in which death occurs. As 
an actual fact modern business conditions are 
such that the average claim is paid in less than 
thirty days after receipt of satisfactory proofs 
of death. Although an estate passes to the re- 



40 INHERITANCE TAX CALCULATIONS. 

mainderman immediately upon the death of the 
life tenant, the same method of calculation (being 
prescribed by statute) is followed, and in conse- 
quence there will always be this slight difference 
between the present value of the life estate plus 
the present value of the remainder and the ap- 
praised value of the testator's estate. Eoughly 
speaking, it may be placed at about five months' 
interest on the estate. There is, of course, a 
mathematical expression which will enable us to 
find the present value of a remainder payable im- 
mediately upon the decease of the life tenant. 
This expression is 

Although this will have practically no effect on 
the amount of the inheritance tax imposed, it has 
been the practice of some calculators to determine 
the present value of the life estate and deduct this 
value from the testator 's estate, calling' the bal- 
ance the remainder. In this method, of course, no 
discrepancy such as referred to above occurs. 

There is another matter, however, which should 
be called to the attention of the student, as the 
terms of some of the wills which may come before 
him may provide for payments to the life tenant 
monthly or quarterly. 

By turning to the chapter on annuities, it will 
be seen that we provide for the payment only to 
those annuitants or life tenants who survive com- 
pleted periods, i. e., if a life tenant should die one 
year and six months after the testator, she would 
receive but one year's income from the testator's 
estate, the assumption being that the last sum 
payable would be the periodic sum which the life 
tenant or annuitant would be alive to receive. 



INHEEITANCE TAX CALCULATIONS. 41 

It may become necessary, however, to incorporate 
in the present value of a life estate such addi- 
tional fractional parts of a year's income as will 
be due the life tenant from the time that the last 
periodical payment was made until her death. 
This would seem to be the rule in England, for 
Mr. George King in Part II of the Text-Book of 
the Institute of Actuaries (page 185) says: " In 
1738, by 2 Geo. II., c. 19, annuities arising out of 
rents and profits from real estate were made ap- 
portionable ; and in 1834, by 4 & 5 Wm. IV., c. 22, 
and again in 1870, by 33 & 34 Vict., c. 35, the rule 
was extended to all other annuities, except such 
annual sums as are made payable under policies 
of assurance." In New York a somewhat similar 
statute has been enacted, although the Superin- 
tendent of Insurance, in the calculations which he 
makes for inheritance tax purposes, takes no cog- 
nizance of the existence of such a statute, which 
is as follows: 

" Sec. 2720. (Added 1893.) Apportionment of 
rents, annuities and dividends. 

All rents reserved on any lease made after June 
seventh, 1875, and all annuities, dividends and 
other payments of every description made payable 
or becoming due at fixed periods under any in- 
strument executed after such date, or, being a last 
will and testament that takes effect after such 
date, shall be apportioned so that on the death of 
any person interested in such rents, annuities, 
dividends or other such payments, or in the estate 
or fund from or in respect to which the same 
issues or is derived, or on the determination by 
any other means of the interest of any such per- 
son, he, or his executors, administrators or as- 
signs, shall be entitled to a proportion of such 
rents, annuities, dividends and other payments 
according to the time which shall have elapsed 



42 INHEKITANCE TAX CAIjCULATIONS. 

from the commencement or last period of pay- 
ment thereof, as the case may be, including the 
day of the death of such person, or of the deter- 
mination of his or her interest, after making al- 
lowance and deductions on account of charges on 
such rents, annuities, dividends and other pay- 
ments. Every such person or his executors, ad- 
ministrators or assigns shall have the same reme- 
dies at law and in equity for recovering such ap- 
portioned parts of such rents, annuities, dividends 
and other payments, when the entire amounts of 
which such apportioned form part, become due 
and payable and not before, as he or they would 
have had for recovering and obtaining such en- 
tire rents, annuities, dividends and other pay- 
ments, if entitled thereto; but the person liable 
to pay rents reserved by any lease or demise, or 
the real property comprised therein shall not be 
resorted to for such apportioned parts, but the 
entire rents of which such apportioned parts 
form parts, must be collected and recovered by 
the person or persons who, but for this section 
or chapter 542 of the laws of 1875, would have 
been entitled to the entire rents ; and such portions 
shall be recoverable from such person or persons 
by the parties entitled to the same under this 
section. This section shall not apply to any case 
in which it shall be expressly stipulated that no 
apportionment be made, or to any sums made 
payable in policies of insurance of any descrip- 
tion. Added by L. 1893, c. 686. From L. 1875, 
c. 542." 

Similar statutes may have been enacted in other 
States, and the reader, therefore, should ascer- 
tain before making the calculations whether the 
laws contemplate a complete or a curtate life es- 
tate. By the latter term is meant a life estate, 
the payments under which are made to the bene- 
ficiary at periodic times with no allowance or 
apportionment of profits or rents for such periods 



LNIIERITANCE TAX CALCULATIONS. 43 

as may elapse between the periodic payment and 
the death of the life tenant. In none of the tables 
of annuity values issued by the various depart- 
ments for the purpose of calculating inheritance 
taxes, is to be found any allowance for the differ- 
ence between the complete and the. curtate values 
of life estates. 

We have designated the curtate present value 
of a life annuity or life estate by Ux. We shall 
designate the complete value of the same quanti- 

o 

ties by ax. A moment's thought will enable the 
reader to appreciate that the only difference be- 
tween these quantities is the present value of that 
portion of the annual income from the estate 
which is earned between the last periodical pay- 
ment and the beneficiary's death; in other words, 
upon the assumption that the deaths in a year 
occur at equal intervals, it will be equal to the 
value of the single premium of an insurance on 
the life of the beneficiary having a face value 
equal to one-half of the annual periodical pay- 
ment to the life tenant. Since this insurance, how- 
ever, is payable at the moment of the death of 
the beneficiary and not at the end of the policy 
j^ear, we must discount it by half a year's inter- 
est. Expressed as a formula we have 

o 

Ux = ttx + \Ax{l + i)^ 

If by the terms of the will the life tenant is to 
receive the income from the estate semi-annually, 
the value of the complete annuity would be 

while if the life tenant enjoys a quarterly income 
tJifi expression resolves itself into 

a<«=«<^'+ lAx{l + iy^ 



44 INHEBITANCE TAX CALCULATIONS. 

Tkese formulae deal with the adjustments which 
must be made when annuities are to be paid up to 
the time of the death of the life tenant, and they 
carry with them the consideration of another 
feature, viz.: annuities payable at fractional pe- 
riods throughout the year. The consideration of 
this aspect is rendered necessary for a correct 
determination of the values of a'|^ and a'J, by 
which symbols we designate annuities which are 
payable semi-annually and quarterly respectively. 

It has been pointed out in various actuarial text- 
books that an approximate formula for finding 
the addition which must be made to the value of 
an annuity in order to obtain the increase made 
necessary by proportional payments, is 

m — 1 
2m 

in which m represents the number of installments 
at equal intervals throughout the year. If, for 
instance, the annuity were payable twice during 
the year (semi-annually), this fraction would 
become 

2 — 1 _ 1 
4 4 

If the annuity, however, is payable four times a 
year (quarterly) the fraction would become 

4 — 1 _ 3 

8 8 

It must be borne in mind, however, that this is 
not the exact formula, but is an approximation 
which is very commonly used in practice and 
which is accurate enough for all matters pertain- 
ing to inheritance tax calculations. 



Directions to be Followed in Working Out the 
Problems on the Following Pages. 

The numbers in brackets at the beginning of 
each problem have been placed there for the 
purpose of referring the reader to the formula 
in the first part of the book, which is appli- 
cable to the solution of each particular prob- 
lem, and it is urgently recommended that before 
attempting to work out any problem the reader 
familiarize himself with the explanations in the 
first part. The Equal Ages method is applicable 
to the problems involving the American and the 
Carlisle Tables of Mortality. Should the reader, 
however, desire to work out a joint life problem 
on the Combined Table of Mortality or the North- 
ampton Table, he must employ the figures ap- 
plicable to those tables, and which have been 
worked out for the various combinations of ages. 
If, for instance, the age of the younger life is 30 
and that of the older is 40, he can obtain the figure 
by direct reference to the table. If, however, the 
exact age is not given, he must obtain his figures 
by finding the place in the table which such ar- 
rangement of ages would occupy. To illustrate r 
If the younger age be 20 and the older 37, he 
would find that these combinations would not be 
given. He has, however, the combinations for 
ages 20 and 35 and ages 20 and 40. He knows, 
therefore, that the combination of 20 and 37 must 
lie between the other two combinations, and by 
simply adding or subtracting (as the case may 
be) two-fifths of the difference to the 20-35 com- 

[451 



46 INHEEITANCE TAX CALCULATIONS. 

bination, the desired result is easily obtained. 
Problem 9a has been worked out by this method 
and clearly explains the system. 

A few general rules for the guidance of those 
working out problems similar to the ones to be 
found on the following pages, may prove useful. 

First: Carefully note the table of mortality 
and the rate of interest which are to be used, and 
ascertain the location of such tables in the third 
part of this book. 

Second: After finding the formula which is 
applicable to your purpose, be sure that you un- 
derstand the method of using it. The explana- 
tion in the first part of the book will enable you 
to readily accomplish this. 

Third : Be sure of the accuracy of your arith- 
metical operations. 

Fourth: Compare the solution of your prob- 
lem with the result obtained by the solution of 
the similar problem given in this book. If, for 
instance, ages 20 and 30 have been used in the 
problem worked out on the following pages, and 
the ages in the problem which you desire to solve 
are 20 and 35, the results obtained should be rela- 
tively close. The ages given in the problems cited 
have been selected with the view of setting forth 
conditions which are likely to occur in practice, 
and the results obtained will, therefore, serve as 
standards of comparison. 

It is thought the explanations given will enable 
the reader to successfully obtain the solution of 
any problem which may arise in his general prac- 
tice. If, however, a difficulty should be met, the 
writer will be pleased, upon receipt of inquiries, 
to offer such suggestions as will clear up such 
difficulties. 



IKHEEITANCE TAX CALCULATIONS. 47 

[3] Problem 1. To determine the value of a life 
estate. 

A dies leaving a widow whose age at the 
time of his death is 49. The report of the 
appraisers shows that the testator's estate at 
the time of his death was $12,500, and by the 
terms of his will his widow is to have the use 
of this estate for life. What is the value of 
said life estate on the basis of the American 
Experience Table of Mortality with 5^ in- 
terest? 

Solution. 

The annual income from the estate is 

$12,500 X .05 = $625 
Applying Formula [3] we have 

From Table XXX we obtain the nec- 
essary values to substitute 

77074.1779 ^u onnvK 
6476. 4069 =^^^-^QQ^^ 

.". The present value of $625 per an- 
num during the lifetime of a person aged 49 is 

11.90076 X $625 = $7,437.98 

Note. The same result may be obtained in 
a shorter manner by direct reference to Table 
XXXI which shows the present value of an 
annuity of $1 at various ages. 

[4] Problem 2. To determine the value of an 
estate for a term of years. 

A desires to provide an income of $500 a 
year for his daughter B for 10 years after his 
death, the income to cease in the event of her 
death prior to the completion of that period. 
B is 20 years old at the time of A's death. 
Required the present value of B's estate ac- 



48 INHERITANCE TAX CALCULATIONS. 

cording to the American Experience Table 

of Mortality with 5^ interest. 

Solution. 

Applying Formula [4] 

■Na;^ JMa:+l+n -"^ 21 -^31 

Obtaining the necessary values from 
Table XXX we have 

557106.5542 — 298202.3543 258904.1999 „ . , ^ 

— 7.415 



34913.9107 34913.9107 

.*. The present value of an annuity of 
$500 per annum for 10 years on a person 
aged 20 is 

$500 X 7.415 = $3,707.50 

N. B. The attention of the student is 
directed to the difference between the term 
' ' annuity ' ' as employed in this book and the 
term ' ' annuity certain ' ' frequently used by 
writers on financial subjects. The latter term 
involves no mortality factor and is merely 
" an obligation to pay a definite amount of 
money each year for a fixed period of time, ' ' 
while the former implies a contract which is 
terminated or modified by the death of the re- 
cipient of the annual payments. 

[5.] Problem 3. To determine the value of a life 
estate, the enjoyment of which is postponed 
until a certain number of years have elapsed 
after the testator's death. 

A dies leaving a will which provides that 
when his daughter B reaches the age of 20, 
she is to receive the sum of $750, and on each 
succeeding anniversary of that date she is to 
receive a similar sum as long as she shall live. 
B is 15 years old at the time of the death 
of the testator. Required the present value 



INHERITANCE TAX CALCULATIONS. 49 

of B's estate according to the American Ex- 
perience Table of Mortality with 5^ interest. 

Solution. 

Applying Formula [5] 

Obtaining the necessary values from 
Table XXX we have 

592020.4649 , 
46314.7314 ^^-'^^^^^ 

.'. The present value of a deferred 
annuity of $750 per annum payable as above is 

$750 X 12.782552 = $9,586.91 

[6.] Problem 4. To determine the present value 
of an estate, the enjoyment of which is post- 
poned until a certain number of years after 
the death of the testator and is then to con- 
tinue only for a limited period. 

A dies leaving to his daughter B an annuity 
of $500 a year, the first payment of which 
is not to be made until 5 years after his death, 
and the succeeding payments are to be made 
only for 20 years if B shall survive that 
period; otherwise the payments are to cease 
with her death. B is 30 years old at the time 
of the death of the testator. Required the 
present value of B's estate according to the 
American Experience Table of Mortality with 
5^ interest. 

Solution. 

Applying Formula [6] 

Ng^„ Nj;^„^m _ N35 N55 

"5; d;^ 



50 INHERITANCE TAX CALCULATIONS. 

Obtaining the necessary values from 
Table XXX we have 
229545.7567—50157.8888 _ 179387.8679 ^ q ny.-, 440 
19769.1207 19769.1207 

. '. The present value of a deferred tem- 
porary annuity of $500 per annum payable 
as above is 

$500 X 9.0741448 = $4,537.07 

[3] Problem 5. To determine the present value 
of a wife's dower. 

A dies intestate. The net income arising 
from his real estate is $9,000 per annum. At 
the time of his death his widow B is 47 years 
old. Required the present value of B 's dower 
according to the Carlisle Table of Mortality 
with 5^ interest. 

Solution. 

B has a one-third dower right in the 
income of $9,000, or $3,000. 

Applying Formula [3] 

D^. D„ 

Obtaining the necessary values from 
Table X, we have 

5697.0710 , 
463.1550 ~ ^"^-"^^^ 
.'. The present value of B's dower 
right is 

$3,000 X 12.301 = $36,903.00 

Note.— The same result may be obtained in 
a shorter manner by direct reference to Table 

XI where the various combinations of — f^ 

have been worked out. 



INHEEITANCE TAX CALCULATIONS. 51 

[3] Problem 6. To determine the present value 
of a husband's estate by curtesy. 

B dies intestate. The net income arising 
from her real estate is $5,000 per annum. At 
the time of her death her husband A is 38 
years old.^ Required the present value of A's 
estate by curtesy, according to the Carlisle 
Table of Mortality, with 5^ interest. 

Solution. 

Using the same formula as in the 
preceding problem 













Obtaining the 


necessary 


values from 


Table X 


we have 




. 




11139.0985 


= 1.^ fiP.^ 





813.4082 — •— " 
.*. The present value of A's estate by 
curtesy is 

$5,000 X 13.695 = $68,475.00 
See the note in the preceding problem. 

[7] Problem 7. To determine the value of an es- 
tate, the enjoyment of which is to cease upon 
the first death of two beneficiaries. 

A dies leaving an estate worth $100,000. 
By the terms of his will his two sons B and C 
are to share equally in the income from his 
estate until one of them dies. At the time 
of A's death B is 28 and C is 32. Required 
the present value of the joint estate of B 
and C according to the American Experience 
Table of Mortality with 5^ interest. 

Solution. 

The first thing to do is to determine 
the equal ages which are the equivalent of 



52 INHERITANCE TAX CALCULATIONS. 

the two ages 28 and 32. From Table III we 
find that 

The force of mortality .at age 28 = . 00821 
The force of mortality at age 32 = . 00853 



2 ) .01674 
.00837 

By consulting the same table we sere 

that .00837 lites between ages 30 and 31, for 

at age 30 the force of mortality is .00835 and 

at age 31 it is .00843, or a difference of 

.00008 for the year. 

.".. .000837 = age 30 + .00002, the latter 

,., ,. .00002 . „ 

quantity representing „,,„- or i or a year. 

The equivalent equal ages of ages 
28 and 32 are therefore ages 30.25 and 30.25. 

The income from the estate is $5,000 
per annum. By reference to Table XXXIII 
we find that the present value of an annuity 
of $1 per annum payable during the joint ex- 
istence of two lives aged 30 is $12.984788, and 
where the two lives are aged 31 the value is 
$12.864782, the difference being $.120006. 
.'. For two lives aged 30i years the value 
must be $12.984788 — .030001 = $12.954787 
for each dollar of annuity and for an annuity 
of $5,000 it will be $64,773.93. 

[8] Problem 8. To determine the value of a 
joint life estate the enjoyment of which is to 
continue until the last survivor dies. 

A dies leaving an estate of $75,000. By the 
terms of his will his two sons B and C are to 
enjoy the income arising from this estate, 



INHEBITANCE TAX CALCULATIONS. 53 

share and share alike during their joint lives, 
and when one of them dies the survivor is 
to enjoy the entire income as long as he shall 
live. At the time of their father's death B 
is 25 and C is 30. Required the present value 
of this bequest according to the American Ex- 
perience Table of Mortality with 5^ interest. 

Solution. 

By referring to the discussion prior 
to the derivation of Formula [8] we find that 
the value sought is the sum of the two annui- 
ties on the single lives minus the joint life 
annuity. From Table XXXI we find that 
at age 25 the value of an annuity of $1 on a 
single life is $15.57033, and at age 30 it is 
$15.08425. By a similar process to that out- 
lined in Problem 7 we ascertain that the 
equivalent equal ages of 25 and 30 are 274 
and 27f . From Table XXXIII we derive 
the value of an annuity of $1 payable during 
the joint existence of two lives aged 27f 
which is $13.223267. Therefore an annuity of 
$1 payable under the conditions mentioned in 
the problem would be $15.57033 + $15.08425 
— $13.223267, which equals $17.431313. As 
the annual income from the estate, however, 
is $3,750 we must multiply that figure by 
17.431313 in order to obtain the answer to the 
problem, $65,367.42. 

[9] Problem 9. To determine the value of a life 
estate, the enjoyment of which is to • begin 
after the death of a certain individual. 

A dies providing in his will that his son Y 
is to receive $500 per annum as long as he 
shall live, the first payment, however, not to 



54 INHEKITANCB TAX CALCULATIONS. 

be made until one year after X, the testator's 
widow, shall die. At the time of A 's death X 
is 52 years old and Y is 31 years old. Re- 
quired the present value of Y's estate accord- 
ing to the Carlisle Table of Mortality with 
6^ interest. 

Solution. 

From Formula [9] we learn that the 
value of Y's interest may be represented by 

dy dxy 

By referring to Table XVH 
ch = 12.94:2 
and by using the Equal Ages Method, as 
explained in preceding problems, we find that 
a^!, = 9.1683 
The present value of an annuity of 
$1, therefore, payable as long as Y shall live, 
the first payment of which shall not begin 
until one year after X shall die, is 
$12,942 — $9.1683 = $3.7737 
And an annuity of $500 is, therefore, worth 
$3.7737 X 500 = $1,886.85 

Problem 9a. In order to explain the method 
which is to be followed in problems employing 
the Actuaries' (or Combined) and the North- 
ampton Tables of Mortality, the above prob- 
lem is worked on the basis of the Actuaries' 
Table of Mortality with 4^ interest, all the 
other conditions remaining the same. 

Solution. 

We apply the same formula a-u — axr 
From Table XXIV we find that 

a» = 16.872 



INHERITANCE TAX CALCULATIONS. 55 

From Table XXV we find that the 
present value of a joint life annuity for $1 
for two lives aged 52 and 27 is $10,849, and 
for two lives aged 52 and 32 it is $10,708. 

062 and 27 = 10 . 849 

052 and 32 = 10.708 



The difference equals .141 

To get the combination of ages (52 
and 31) in the problem we must add ^ of 
the difference to aga and 30. | of .141 = .028, 
and adding this to 10.708 we obtain 10.736 as 
the approximate value of 

^52 and 31 
Proceeding as before 
16.872 — 10.736 = 6.136 
and for an annuity of $500 it will, therefore, 
be 

• 6.136 X $500 = $3,068.00 
N. B. — The difference between the results 
of problems 9 and 9a is due to the fact that 
the former is on a 6^ basis while the latter is 
on a 4^ basis. 

[10] Problem 10. To determine the present value 
of each beneficiary's share in a joint estate 
the income of which is to be divided equally 
between them during their joint existence, the 
entire income to go to the survivor as long as 
he shall live. 

A dies leaving an estate of $75,000. By the 
terms of his will his two sons X and Y are to 
enjoy the income arising from this estate, 
share and share alike during their joint exist- 
ence, and when one of them dies the survivor 



56 INHERITANCE TAX CALCULATIONS. 

is to enjoy the entire income as long as he 
shall live. At the time of their father's death 
X is 25 and Y is 30. Required the present 
value of X's interest in this estate and of 
Y's interest according to the American Ex- 
perience Table of Mortality with 5^ interest. 

Solution. 

From the Formula we learn that X's 
interest in the above annuity would be the 
difference between the single annuity on his 
life and one-half the joint annuity on his life 
and Y's. From Table XXXI the present 
value of an annuity of $1 on a life aged 25 
is $15.57033, and deriving the joint life an- 
nuity in the method outlined in Problem 7 we 
find that one-half of it equals $6.611633. The 
annual income of the estate is 5^ of $75,000, 
or $3,750. We must multiply this figure by 
the difference between the two annuities. 

.'. X's interest = $3750 (15.57033 — 
6.611633)= $33,595.11. 

And by a similar process of reason- 
ing we can ascertain that Y's interest = 
$3750 (15.08425 — 6.611633)= $31,772.31. 

It will be apparent that the terms of 
this problem are similar to those of Problem 
8, and the proof will be, therefore, in ascer- 
taining whether the interest of X plus the 
interest of Y will equal the entire value of 
the estate. We have seen that 

X's interest = $33,595.11 

Y's interest = 31,772.31 



Total = $65,367.42 
which is the exact result obtained in the solu- 
tion of Problem 8. 



IKHEKITAKCE TAX CALCULATIONS. 57 

[11] Problem 11. To determine the present 
value of an estate the income of which is to 
be paid to the survivor of two designated in- 
dividuals so long as he shall live. 

F dies leaving an estate worth $25,000 and 
a will providing that the income therefrom is 
to go to a charitable organization until one 
of his two sons X and Y dies. When that 
event occurs the survivor is to enjoy the en- 
tire, proceeds of the estate until his death. 
The age of X at the time of the testator's de- 
cease is 30 years and the age of Y is 25 years. 
Required the present value of the bequest 
according to the American Experience Table 
of Mortality with 5^ interest. 

Solution. 

By referring to Formula [11] we 
learn that this present value is equal to the 
single annuity on X's life plus the single 
annuity on Y's life minus twice their joint life 
annuity. The derivation of these values has 
been explained in the preceding problems, so 
the outline of the work only will be given. 

Annuity on X's life for $1 = $15.08425 

Annuity on Y's life for $1 = $15.57033 

Joint annuity on X and Y 
for $1 = $13.223267 

The annual income of the estate is 
5^ of $25,000, or $1,250. We must, therefore, 
multiply this figure by the sum of the single 
annuities diminished by twice the joint an- 
nuity. 

The solution of the problem, there- 
fore is 
$1250 ( 15.57033 -f 15.08425— 26.446534)= $5,260.06 



58 INHERITANCE TAX CALCULATIONS. 

[9] Problem 12. To determine tlie present value 
of an inchQate right of dower. 

X, aged ^0, is the owner of real estate 
value at $150,000. His wife, Y, is aged 38. 
Required the present value of Y's inchoate 
dower right according to the Carlisle Table 
of Mortality with 5^ interest. 

Solution. 

This is practically the same as Prob- 
lem 9 and can be solved by the same formula. 

From Table XI we find that ay = 
13.695, and applying the Equal Ages Method 
we obtain from Table XIII the value of a^y as 
11.2291. 

Therefore 13.695 — 11.2291 -= 2.4659 
or the present value of 1 unit payable in the 
manner indicated above. As this problem in- 
volves dower rights we must take i of the 
income on the estate of $150,000 which is 
$2,500 per annum and multiply this by 2.4659 
in order to obtain the answer $6,164.75. 

[13] Problem 13. To determine the value of a 
life estate, the income of which is to be di- 
vided share and share alike among three 
designated beneficiaries until one only shall 
survive, when the entire income is to go to 
him until his death. 

F dies leaving an estate of $200,000. Each 
of his three sons, X, Y, and Z, is to get i 
of the net annual income of this estate until 
one of them shall die, at which time the two 
survivors are each to receive i of said in- 
come. After the second of these designated 
individuals dies, the entire net income is to 



INHERITANCE TAX CALCULATIONS. 59 

be enjoyed by the survivor until his death. 
X, Y, and Z are 30, 28, and 23 years of age 
respectively. Eequired the present value of 
this estate according to the American Experi- 
ence Table of Mortality with 5^ interest. 

Solution. 

An annuity on the longest of three 
lives may be determined from Formula [13]. 

Ux -\- Uy -\- Oz ttxy Qixi: Oipz ~r Oxyi 

Proceeding as in the other problems 
we find the following values for each of the 
quantities : 
a^ =$150,842.50 a^„ =$130,847.29 

ay = 152,921.00 a^, = 132,975.38 

a. = 157,355.20 a:,^= 134,301.15 

axv.= 117,684.39 

Substituting these values in the 
above formula the final result will be $180,- 
679.27. 

[14] Problem 14. To determine the present 
value of an estate to be enjoyed as long as 
two of three designated individuals are living. 

^ F dies leaving an estate of $100,000. His 
three sons, X, Y, and Z, are to share equally 
in the income arising from this estate until 
there is but one of them surviving, when the 
annuity ceases. X, Y, and Z are 40, 37, and 
30 years of age respectively. Eequired the 
present value of this estate according to the 
American Experience Table of Mortality with 
5^ interest. 

Solution. 

Applying Formula [14] 

Q/xy ~p (Zys ~p Qfxs — — Zdxys 

will give the desired result. 



60 INHERITANCE TAX CALCULATIONS. 

Proceeding as in the other problems^ 
we obtain the following values for each of 
the quantities : 

a.y = $58,773.73 

Oy. = 62,293.25 

a,, = 60,684.80 

2aa:v. = 106,179.73 

Substituting these values in the 
above formula, we obtain the final result 
$75,572.05. 

[15] Problem 15. To determine the value of an 
estate, the enjoym'ent of which by a desig- 
nated individual is not to take place until the 
first death between two other designated in- 
dividuals. 

K dies leaving an estate appraised at 
$500,000. One of the terms of his will is that 
the net income from this estate shall be paid 
to the two brothers of the testator, Y and Z, 
until one of them shall die. When that event 
occurs the testator's son X, if then living, 
shall receive the net income from the estate 
for the balance of his life. At the time of 
K's death X was 30, Y was 54, and Z was 58. 
Required the value of X's contingent life es- 
tate according to the American Experience 
Table of Mortality with 5^ interest. 

Solution. 

Applying Formula [15], which is 



we are enabled to obtain the value of ax di- 
rectly from Table XXXI. The value of a^vz 
must be worked out in the manner alreadv 



INHERITANCE TAX CALCULATIONS. 61 

described to obtain the equivalent equal ages, 
and the value of the annuity can then be ob- 
tained by inspection from Table XXXV. 

a^ = 15.08425 

aa=y.= 7.303537 

. ". a. — a:r„.=15.08425— 7.303537==7.780713 

And since the income on $500,000 at 5^ is 
$25,000, the final result is 

7.780713 X $25,000 = $194,517.83 

[16] Problem 16. To determine the value of an 
estate, the enjoyment of which by a desig- 
nated individual is not to take place until the 
death of both of two other designated indi- 
viduals. 

K dies leaving an estate appraised at 
$500,000. One of the terms of his will is that 
the net income arising therefrom shall be paid 
each year to the testator's two brothers, Y 
and Z, share and share alike. After the death 
of one of these brothers, the entire income is 
to go to the survivor until his death. When 
both Y and Z are dead the net income is to go 
each year to the testator's son X, if he be 
then alive. At the time of K's death X, Y, 
and Z are aged 30, 54, and 58 years respec- 
tively. Required the present value of the 
estate of X according to the American Ex- 
perience Table of Mortality with 5^ interest. 

Solution. 

This being a little more complicated 
problem every step will be worked out. 

To this problem Formula [16] is 
applicable : 

Ct/x O/xy Ofxz "P Clxyz 



62 INHEKITANCE TAX CALCULATIONS. 

The first step is to find the equiva- 
lent eqnal ages. From Table III we find the 
force of mortality at age 30 = . 00835 
and the force of mortality at age 54 = . 01712 

2 ) .02547 
.01273 

Inspecting Table III we see that the 
nearest approach to .01273 is at age 48, where 
the force of mortality is .01265, or a differ- 
ence of .00008. Now inasmuch as the differ- 
ence between the force of mortality at ages 
48 and 49 is .00056, it follows that .00008 is 
I of the difference, and therefore .01273 
represents the force of mortality at age 
48|, , from which we are enabled to state 
that two lives aged 30 ^and 54 are the equiv- 
alent of two lives both aged 48y years. 
From Table XXXIII we see that the present 
value of an annuity of $1 on two lives aged 

48 is 9.856660, while the present value at age 

49 is 9.620863., .235797 is the difference for 
1 year and the difference for ^ of a year is 
.033685, which, subtracted from 9.856660, 
gives 9.822975 as the present value of a joint 
life annuity on two lives both aged 48^- years. 

.". «.„ = 9.822975 
The derivation of the value of axz is 
done in a similar manner, and there will be 
no necessity for explaining each step. 
Force of mortality at age 30= .00835 
Force of mortality at age 58= .02212 



2 ). 03047 
.01523 



INHEBITANCE TAX CALCULATIONS. 63 

.01523 equals the force of mortality 
at age 51|f or 51x*Tr approximately. There- 
fore the value of 

0^3 = 8.902938 
We obtain the value on three lives in 
a similar way. 
Force of mortality at age 30= .00835 
Force of mortality at age 54 = . 01712 
Force of mortality at age 58= .02212 



3 ). 04759 
.01586 
which equals the force of mortality at age 
52|| or age 52.64 approximately. To obtain 
the value of the annuity on three live^ we 
must use Table XXXV, from which we find 
that at age 52.64 the value of 
ax»3 = 7.303537 
The value of a^ is obtained directly 
from Table XXXI, and substituting these 
values in the formula, we have 
15.08425 — 9.822975 — 8.902938 + 7.303537 
which gives $3.661874 as the present value of 
an annuity of $1 on X 's life payable as stated. 
For an annual income of $25,000, therefore, 
it will be 

$25,000 X 3.661874 = $91,546.85 

[17] Problem 17. To determine the present 
value of an estate the enjoyment of which by 
two designated individuals is not to com- 
mence until after the death of a third desig- 
nated individual, 

G dies leaving an estate of $25,000. By 
the terms of his will his two daughters, Y and 



64 INHERITANCE TAX CALCULATIONS. 

Z, are to receive the income from the estate 
during their joint existence, no payments, 
however, to be made until after the death of 
the testator's son X. X, Y, and Z are 40, 30, 
and 28 years of age respectively. Eequired 
the present value of this estate according to 
the American Experience Table of Mortality 
with 5^ interest. 

Solution. 

The present value of this estate is 
ayz — axyz (Formula [17]) 
Solving this as in the preceding 
problem we find 
avz = l^. 084729 and a.v. == 10 . 963674 

Substituting these values 
13 . 084729 — 10 . 963674 = 2 . 121055 
and multiplying this by the annual income 
from the estate, we have for our final result 
2 . 121055 X $1,250 = $2,651 . 32 

[18] Problem 18. To determine the value qf an 
estate to be enjoyed by the survivor of two 
designated individuals after the death of a 
third designated individual. 

H dies leaving an estate of $100,000, and a 
widow Z, a son X, and a daughter Y. On the 
death of Z the income thereof is to be divided 
equally between X and Y if both survive Z, 
and on the death of either of them the entire 
income is to go to the survivor. If but one 
survive Z the entire income is to go to such 
survivor. X, Y, and Z are 28, 20, and 54 
years of age, respectively. Eequired the 
present value of the estate of X and Y accord- 
ing to the Carlisle Experience Table of Mor- 
tality with 6^ interest. 



INHERITANCE TAX CALCULATIONS, 65 

Solution. 

These conditions may be solved hj 
applying Formula [18]. 

Ox ~r Oy Qxy Ctxn: Oyz ~r Oixyz " ' 

Proceeding as in previous problems 
we find from Table XVII 

ax = Vi. 182 and a„ -= 13 . 835 
and by the Equal Ages Method (being sure 
to use the tables derived from the Carlisle 
Experience) we have 

axy =11.7688 
axz.= 8.9077 
ayz = 9.3229 
axyz= 8.5369 
Substituting these values we have 

13.182 + 13.835 — 11.7688 — 8.9077 — 9.3229 + 8.5369 = 5.5545 

Multiplying this by the yearly annuity, we 
have 

5.5545 X $6,000 == $33,327.00 

N. B. — In finding the equivalent equal ages 
be sure to use that portion of Table III de- 
rived from the Carlisle Mortality Table. 

[19] Problem 19. To determine the value of an 
estate, the income of which is to be divided 
equally between the two survivors of three 
designated individuals and is to continue dur- 
ing their joint existence only. 

H dies leaving an estate of $200,000, the 
annual income of which is, on the first death 
among his three children, X, Y, and Z, to be 
divided between the two survivors of them, 
said, survivors to receive such income until 
either one of them dies. X, Y, and Z are aged 
40, 38, and 36 years respectively. Required 
5 



66 INHEKITANCE TAX CALCULATIOKS. 

the present value of the estate according to 
the American Experience Table of Mortality 
with 5^ interest. 

Solution. 

Formula [19] applies to this case: 

Deriving these values we have 
a^y =11.678982 
a.. =11.822495 , 
oy. =12.019470 
a.„. = 10.354367 
Substituting in the formula 
11.678982 + 11.822495 + 12.019470—31.063101 
which equals 4.457846, and multiplying this 
by the annual income from the estate we have 
4.457846 X $10,000 = $44,578.46 

[20] Problem 20. To determine the interest 
which a third designated individual has in 
an estate of two other designated individuals. 

F dies leaving an estate of $100,000. By 
the terms of his will his two sons, X and Y, 
are to receive an annuity amounting to the 
income from his estate. If either of them 
dies before the testator's sister, Z, the sur- 
vivor is to share the annuity with her as long 
as she shall live. X, Y, and Z are 21, 26, and 
50 years of age respectively. Required the 
present value of Z's interest in this estate 
according to the American Experience Table 
of Mortality with 5^ interest. 

Solution. 

By reference to Formula [20] we 
find that Z's interest is represented by 



ISHEKITANCK TAX CALCULATIONS. 67 

Proceeding as before we find that 

axz =10.768059 
ay, =10.708773 
axv.= '9.917408 

Substituting these values in the for- 
mula we have 

5.384029 + 5.354386 — 9.917408 = .821007 

Multiplying this by the amount of 
the annuity we have 

.821007 X $5,000 = $4,105.04 

[21] Problem 21. To determine the present 
value of the interest which a designated in- 
dividual has in an estate, the income of which 
is to be divided equally among three desig- 
nated individuals so long as they are all liv- 
ing, and after the decease of any one of them, 
is to be divided equally between the two sur- 
vivors as long as they shall both be alive. 

H dies leaving an estate of $50,000, the in- 
come of which is to be divided equally be- 
tween his three daughters, X, Y, and Z, as long 
as they shall all be alive. Upon the death 
of any one, the remaining two shall divide 
the income from the estate between them as 
long as they shall both be alive, i. e., during 
their joint existence. X, Y, and Z, are 35, 32, 
and 27 years of age respectively. Required 
the value of X's interest in this estate accord- 
ing to the American Experience Table of 
Mortality with 5^ interest. 

Solution. 

The solution of this will depend upon 
the application of Formula [21]. 

iOxy ~r idme g Oixy» 



68 INHERITANCE TAX CALCULATIONS. 

Proceeding as before we find these 
quantities to be 

a.y =12.527095 
a^. =12.764094 
a^„. = 11.274784 
Substituting 
6.263547 + 6.382047 — 7.516522 = 5.129072 
and multiplying this by the income we get 
for X's share 

5.129072 X $2,500 = $12,822.68 

[22] Problem 22. To determine the present 
value of the interest of one of two designated 
individuals in an estate, the enjoyment of 
which is to be postponed until a third desig- 
nated individual's death, after which the in- 
come from the estate is to be divided equally 
between the two individuals as long as they 
shall both live, and then to go to the survivor 
as long as he shall live. 

F dies leaving an estate of $75,000. Upon 
the death of his widdw X the income from 
his estate is to be divided equally between 
his two sons, Y and Z, as long as they shall 
both live, and to the survivor of these two 
shall be paid the entire income as long as he 
shall live. X, Y, and Z are 60, 35, and 31 
years of age respectively. Required the pres- 
ent value of Y's interest in this estate accord- 
ing to the Carlisle Experien.ce Table of 
Mortality with 5^ interest. 



Solution. 
We 

QUli 
Oy Ctxy ittyn -\- ^Ctxyz 



Solution. 

We may obtain a solution by apply- 
ing Formula [22]. 



INHEEITANCE TAX CALCULATIONS. 69 

From T.; ^-^lo XI we obtain 

0, = 14.127 
Obtaining che other values as before, 
we have 

a., J =-- 8.2775 
a. =12.1185 

aa:y.= 7.6498 

Substituting these values in the for- 
mula, we have 
14.127 — 8.2775 — 6.0592 + 3.8249 = 3.6152 

Multiplying this by the income from 
the estate we shall have 

3.6152 X $3,750 = $13,557.00 
which is the value of Y's interest. 

f23] Problem 23. To determine the present 
value of the interest of a designated individ- 
ual in an estate which is to be divided equally 
between two designated individuals during 
their joint existence; after the first death be- 
tween them said income is to be divided 
equally between the survivor of them and a 
third designated individual (if the latter be 
then living) during their joint existence; at 
the first death of the latter two the entire in- 
come is to go to the survivor of them. If said 
third designated individual be not living at 
the first death between the first two desig- 
nated individuals, then the entire income of 
the estate is to go to the survivor of said first 
two for life. 

Gr dies leaving an estate of $100,000. The 
income from this estate is to go to his two 
sons, X and Y, as long as they shall both be 
living, share and share alike, and after the 



70 INHERITANCE TAX CALCULATIONS. 

first death between them the income from the 
estate is to be divided equally between the 
survivor and Z, the testator's adopted daugh- 
ter, if the latter be then living, and the entire 
income is to go to the survivor of the lattei- 
two. If Z be not then living the entire income 
is to go to the survivor of X and Y for life. 
X, Y, and Z are 33, 30, and 20 years of age 
respectively. Required the value of X's in- 
terest in this estate according to the Ameri- 
can Experience Table of Mortality with 5^ 
interest. 

Solution. 

This may be solved by means of 
Formula [23] which is. 

Proceeding as in the former prob- 
lems, we find 

a. =14.73492 
a;.y =12.789266 
te =13.153709 
aa;v. = 11.589646 

Substituting these values in the 
formula 

14.73493 — 6.394633 — 6.576854 -|- 5.794823 = 7.558256 

and the value of X's interest is, therefore, 
7.558256 X $5,000 = $37,791.28 

[24] Problem 24. To determine the value of a 
vested remainder. 

F dies leaving an estate worth $25,000 
which he devises to his widow X for life, with 
the remainder over to his son. At the time 
of the testator's death X is 53 years old. Re- 
quired the present value of the remainder 
according to the Combined or Actuaries' Ex- 
perience Table of Mortality with 4^ interest. 



INHERITANCE TAX CALCULATIONS. 71 

Solution. 

Applying Formula [24] we have 

M^ ^ M^, ^ 4262.71828 ^ 
D. D,, 8261.89245 

the figures being obtained from Table XXIII, 
This is the value of $1 payable when 
X dies, and the value of the remainder is, 
therefore, 

$25,000 X .51595 = $12,898.75 
Note. — The same result could have been ob- 
tained in a shorter manner by direct reference to 

Table XXIV, where all the values of =r- will be 
found worked out. 

[24] Problem 25. To determine the value of a 
legacy payable upon the dea,th of the life 
tenant. 

G dies leaving an estate to his widow X 
for life. His will likewise provides that upon 
X's death her niece shall receive $5,000. At 
the time of the testator's death X is 48 years 
old. Required the present value of the legacy 
left to X's niece according to the Combined 
Experience Table of Mortality with 4^ in- 
terest. 

Solution. 

This is similar to Problem 24 and 
will be worked out by the short method. 

From Table XXIV we learn that the 
present value of $1 payable upon the death 
of a person aged 48 is $.46002. The present 
value of the legacy mentioned above is, there- 
fore, $2,300.10. 



72 INHERITANCE TAX CALCULATIONS. 

[25] Problem 26. To determine the value of a 
, remainder payable on the first death of two 
designated individuals. 

K dies leaving an estate of $100,000. By 
the terms of his will his two daughters, X and 
Y, are to receive the income of this estate 
during their joint existence. At the first 
death between them the entire estate is to go 
to a charitable institution. At the time of 
their father's death the ages of X and Y are 
30 and 20 years respectively. Eequired the 
present value of the remainder according to 
the American Experience Table of Mortality 
with 5^ interest. 

Solution. 

First determine the equal ages cor- 
responding to 20 and 30 in a similar manner 
to that followed in Problem 7, viz. : 

Force of Mortality at age 20= .00786 
Force of Mortality at age 30= .00835 



2 ). 01621 
.008105 
.008105 = the force of mortality at age 26.3. 

From Table XXXIII we find the 
value of a remainder of $1 payable upon the 
first death of two lives aged 26 is $.3137482, 
and at age 27 it is $.3184575. At age 26.3, 
therefore, it is $.315161, and for an estate of 
$100,000 it is $31,516.10. 

This could also have been worked 
out by applying the commutation columns ta 
the formula. 

but Table XXXIII affords us . a shorter 



INHERITANCE TAX CALCULATIONS. 73 

method, as we have the various values of this 
formula already worked out. 

[26] Problem 27. To determine the value of a 
remainder payable on the death of both of 
two designated individuals. 

B dies leaving an estate of $250,000. The 
income therefrom is to be divided equally be- 
tween his two sons, X and Y, as long as they 
both shall live, and upon the death of one the 
entire income shall be paid to the other as 
long as he shall live. When both X and Y 
have died the estate is to pass to a charitable 
institution. At the time of the testator's 
death the ages of X and Y are 42 and 38 
years respectively. Required the present 
value of the remainder according to the 
American Experience Table of Mortality 
with 5j^ interest. 

Solution. 

From Formula [26] we can see that 
the solution of this problem resolves itself 
into finding the sum of the remainders on each 
of the individual lives and subtracting there- 
from the value of the remainder payable 
upon the first death. 

From Table XXXI the remainder at 
age 38 of an estate of $250,000 is found to be 
$70,964.60, and at age 42 it is $78,984.83. 
Their sum is $149,949.43. By applying the 
Equal Age Method we learn that the equiva- 
lent equal ages of 42 and 38 are 40^. From 
Table XXXIII we learn that the value of $1 
payable upon the first death of two lives aged 
40^ is $.4057102, and for an estate of $250,000 



74 INHERITANCE TAX CALCULATIONS. 

it is, therefore, $101,427.55. The solution of 
the problem is found, therefore, to be 
$149,949.43 — $101,427.55 = $48,521.88 

[27] Problem 28. To determine the value of a 
vested remainder which may be divested. 

B dies leaving an estate of $100,000 to his 
wife X for life with the remainder over to 
her daughter Y, if Y be living at the death of 
X; otherwise the remainder to go to the chil- 
dren of Y. X is 63 years of age and Y is 37. 
Required the value of Y's remainder accord- 
ing to the American Experience Table of 
Mortality with 5^ interest. 

Solution. 

It will be seen that this may be solved 
by Formula [27]. 

From Table II we find that ««=- .97590 
From Table III we find that /*„ = .03220 

In the manner indicated in the pre- 
ceding problems we can find the equal ages 
which are equivalent to 

O/xyj dx-i.y and dx-^-iiV 

Applying Table XXXIII we obtain 
for these values 

a^y =7.539171 
ax_i.» = 7.797691 

a.,+i.« = 7.281828 

Substituting these values in the for- 
mula, we have 

.97590[.03220(7.5.391tl+i)+J (7.797691 — 7.281828)] 



INHEEITANCE TAX CALCULATIONS. 75 

Combining we have 

.97590[.03220(3,039171)+i(.515868)] which equals 
.975»0[.2588613+.2579315] which equals 
.97590(.51«7928) which equals 

.504338 which represents the present value of 
a unit payable at the death of a person aged 
63 if another person aged 37 should then be 
alive. 

The present value of an estate of 
$100,000 is, therefore, 

.504338 X $100,000 = $50,433.80 



TABLES 

OF 

Interest, Discount and Mortality. 



COMMUTATION COLUMNS — SINGLE 

PREMIUMS AND ANNUITIES. 



INDEX TO TABLES. 



Interest Tables. paob. 

Table I. Amount of $1 at the end of various periods. . . 81 

Table II. Present Value of |1 at end of various periods. 84 

Force of Mortality. 
Table III. Carlisle and American Experience Tables of 

Mortality 87 

Northampton Experience. 

Table IV. Table of Mortality m 

Table V. Single Life, Anuuities and Single Premiums, 5^ 93 

Table VI. Two Lives, Annuities and Single Premiums, 5^ 96 

Table VII. Single Life, Annuities and Single Premiums, 6^ 118 

Table VIII. Two Lives, Annuities and Single Premiums, 6% 131 

Carlisle Experience. 

Table IX. Table of Mortality 143 

Table X. Single Life, Commutation Columns, 5% 146 

Table XI. Single Life, Annuities and Single Premiums, 5^ 149 

Table XII. Two Lives, Commutation Columns, 5sf. 153 

Table XIII. Two Lives, Annuities and Single Premiums, 5% 15S 

Table XIV. Three Lives, Commutation Columns, 5% 158 

Table XV. Three Lives, Annuities and Single Premiums, 5^ 161 

Tttble XVI. Single Life, Commutation Columns, 65J 164 

Table XVII. Single Life, Annuities and Single Premiums, 6fl 167 

Table XVIIL Two Lives, Commutation Columns, 6% 170 

Table XIX. Two Lives, Annuities and Single Premiums, 6^ 173 

Table XX. Three Lives, Commutation Colnmns, 6% 176 

Table XXI. ThreeLives.AnnuitiesandSinglePremiums, 6^ 179 

Combined or Actuaries' Experience. 

Table XXII Table of Mortality , 183 

Table XXIIl. Single Life, Commutation Columns, 4^ 185 

Table XXIV. Single Life, Annuities and Single Premiums, 4^ 188 
Table XXV. Two Lives, Annuities and Single Premiums, 4^ 191 

Table XXVL Single Life, Commutation Columns, 5% 211 

Table XXVII. Single Life, Annuities and Single Premiums, 5^ 314 
Table XXVIII. Two Lives, Annuities and Single Premiums, 5^ 217 

[79] 



80 



INDEX TO TABLES. 



Amebican Expekiencb. Paob. 

Table XXIX. Table of Mortality 237 

Table XXX. Single Life. Cominutatioa Columns, 5% 240 

Table XXXI. Single Life, Annuities and Single Premiums, 5^ 243 

Table XXXIL Two Lives, Commutation Columns, 5^ 246 

Table XXXIIL Two Lives, Annuities and Single Premiums, 5^ 249 

Table XXXIV. Three Lives, Commutation Columns, 5% S53 

Table XXXV. Three Lives.Annuities and Single Premiums, 5^ 255 



INTEREST TABLES. 



81 



Table I — Interest Tables. 

Amount of $1 at 4^, 5^, and 6^ at the End of Vari- 
ous Periods. 

Tears. 4% 5% 6% 

1 1,0400 1.0500 1.0600 

2 1.0816 1.1025 1.1236 

3 1.1249 1.1576 1.1910 

4 1.1699 1.2155 1.2625 

5 1.2167 1.2763 1.3382 

6 1.2653 1.3401 1.4185 

7 1.3159 1.4071 1.5036 

8 1.3686 1.4775 1.5938 

9 1.4233 1.5513 1.6895 

10 1.4802 1.6289 1.7908 

11 . 1.5395 1.7103 1.8983 

12 1.6010 1.7959 2.0122 

13 1.6651 1.8856 2.1329 

14 1.7317 1.9799 2.2609 

15 1.8009 2.0789 2.3966 

16 1.8730 2.1829 2.5404 

17 . 1.9479 2.2920 2.6928 

18 2.0258 2.4066 2.8543 

19 2.1068 2.5270 3.0256 

20 2.1911 2.6533 3,2071 

21 2.2788 2.7860 3.3996 

22 2.3699 2.9253 3.6035 

23 2.4647 3.0715 3.8197 

24 2.5633 3.2251 4.0489 

25 2.6658 3.3864 4.2919 

26 2.7725 3.5557 4.5494 

27 2.8834 3.7335 4.8223 

28... 2.9987 3.9201 5.1117 

29... . 3.1187 4.1161 5.4184 

30 3.2434 4.3219 5.7435 

81 3.3731 4.5380 6.0881 

32 , 3.5081 4.7649 6.4534 

6 



82 iNTEEEST Tables. 

Table I — {Continued). 

TeatB. 4% 5% 6% 

33 3.6484 5.0032 6.8406 

34 3.7943 5.2533 7.2510 

35 3.9461 5.5160 7.6861 

36 4.1039 5.7918 8.1473 

37 4.2681 6.0814 8.6361 

38 4.4388 6.3855 9.1543 

39 4.6164 6.7048 9.7035 

40 4.8010 7.0400 10.2857 

41 4.9931 7.3920 10.9029 

42 5.1928 7.7616 11.5570 

43 5.4005 8.1497 12.2505 

44 5.6165 8.5572 12.9855 

45 5.8412 8.9850 13.7646 

46 6.0748 9.4343 14.5905 

47 6.3178 9.9060 15.4659 

48 6.5705 10.4013 16.3939 

49 6.8333 10.9213 17.3775 

50 7.1067 11.4674 18.4202 

51 7.3910 12.0408 19.5254 

52 7.6866 12.6428 20.6969 

63 7.9941 13.2749 21.9387 

54 8.3138 13.9387 23.2550 

55 8.6464 14.6356 24.6503 

56 8.9922 15.3674 26.1293 

57 9.3519 16.1358 27.6971 

58 9.7260 16.9426 29.3589 

59 10.1150 17.7897 31.1205 

60 10.5196 18.6792 32.9877 

61 10.9404 19.6131 34.9670 

62 11.3780 20.5938 37.0650 

63 11.8332 21.6235 39.2889 

64 12.3065 22.7047 41.6462 

65 12.7987 23.8399 44.1450 

66 13.3107 25.0319 46.7937 

67 13.8431 26.2835 49.6013 

68 14.3968 27.5977 52.5774 



INTEBEST TABLES. 



83 





Table I — {Concluded). 




Years. 


4% 


5% 


6% 


69 


14.9727 


28.9775 


55.7320 


70 


15.5716 


30.4264 


59.0759 


71 


16.1945. 


31.9477 


62.6205 


72 


16.8423 


33.5451 


66.3777 


73 


17.5160 


35.2224 


70.3604 


74 


18.2166 


36.9835 


74.5820 


75 


18.9453 


38.8327 


79.0569 


76 


19.7031 


40.7743 


83.8003 


77 


20.4912 


42.8130 


88.8284 


78 


21.3108 


44.9537 


94.1581 


79 


22.1633 


47.2014 


99.8075 


80 


23.0498 


49.5614 


105.7960 


81 


23.9718 


52.0395 


112.1438 


82 


24.9307 


54.6415 


118.8724 


83 


25.9279 


57.3736 


126.0047 


84 


26.9650 


60.2422 


133.5650 


85 


28.0436 


63.2544 


141.5789 


86 


29.1653 


QGAlh 
69.7379 


150.0736 


87 


30.3320 


159.0781 


88 


31.5452 


73.2248 


168.6227 


89 


32.8071 


76.8861 


178.7401 


90 


34.1193 


80.7304 


189.4645 


91 


35.4841 


84.7669 


200.8324 


92 


36.9035 


89.0052 


212.8823 


93 


38.3796 


93.4555 


225.6553 


94 


39.9148 


98.1283 


239.1946 


95 


41.5114 


103.0347 


253.5463 


96 


43.1718 


108.1864 


268.7590 


97 


44.8987 


113.5957 


284.8846 


98.. 


46.6947 


119.2755 


301.9776 


99 


48.5625 


125.2393 


320.0963 


100 


50.5049 


131.5013 


339.3021 



84 



DISCOUNT TABLES. 



Table II — Discount Tables. 

Present Value of $1 at 4^, 5^, and 6^ at me End 
of Various Periods. 

Years. 4% 5% 6% 

i 980588 .975906 .971286 

1 961538 .952381 .943396 

2 924556 .907029 .889996 

3 888996 .863838 .839619 

4 854804 .822702 .792094 

5 821927 .783526 .747258 

6 790315 .746215 .704961 

7 759918 .710^681 .665057 

8 730690 .676839 .627412 

9 702587 .644609 .591898 

10 675564 .613913 .558395 

11 649581 .584679 .526788 

12 624597 . 556837 . 496969 

13 600574 .530321 .468839 

14 577475 .505068 .442301 

15 555265 .481017 .417265 

16 533908 .458112 .393646 

17 513373 .436297 .371364 

18 493628 .415521 .350344 

19 474642 .395734 .330513 

20 456387 .376889 .311805 

21 438834 .358942 .294155 

22 421955 .341850 .277505 

23 405726 .325571 .261797 

24 390121 .310068 .246979 

25 375117 .295303 .232999 

26 360689 .281241 .219810 

27 346817 .267848 .207368 

28 333477 .255094 .195630 

29 320651 .242946 .184557 

30 308319 . 231377 . 174110 

31 296460 . 220359 . 164255 

32 ,. . .285058 .209866 .154957 



DISCOUNT TABLES. 



85 



Table II — (Continued). 

Tears. 4% 5% 6% 

33 274094 .199873 .146186 

34 263552 .190355 ,137912 

35 253415 .181290 ,130105 

36 243669 .172657 .122741 

37 234297 .164436 .115793 

38 225285 . 156605 . 109239 

39 216621 . 149148 . 103056 

40 208289 .142046 .097222 

41 200278 .135282 .091719 

42 192575 .128840 .086527 

43 185168 .122704 .081630 

44 178046 .116861 .077009 

45 171198 .111297, .072650 

46 164614 .105997 .068538 

47 158283 .100949 ,064658 

48 152195 .096149 .060998 

49 146341 .091564 .057546 

60 140713 .087204 .054288 

51 135301 ,083051 ,051215 

52 130097 .079096 .048316 

53 125093 .075330 .045582 

54 1202821 .071743 .043001 

55 115656 .068326 .040567 

56 111207 .065073 .038271 

57 106930 .061974 .036105 

58 102817 .059023 .034061 

59'. 098863 . 056212 . 032133 

60 095060 .053536 .030314 

61 091404 .050986 .028598 

63 087889 .048558 .026980 

63 084508 .046246 .025453 

64 081258 .044044 .024012 

65 078133 .041946 .022653 

66 075128 .039949 .021370 

67 072238 . 038047 . 020161 

68 069460 .036235 .019020 



86 



DISCOUNT TABLES. 



Table II — {Concluded). 

■Sears. 4% 5% 6% 

69 066788 .034509 .017943 

70 064219 .032866 .016927 

71 061749 .031301 .015969 

72 059374 .029811 .015065 

73 057091 .028391 .014213 

74 054895 .027039 .013408 

75 052784 .025752 .012649 

76 050754 .024525 .011933 

77 048801 .023357 .011258 

78 046924 .022245 .010620 

79 045120 .021186 .010019 

80 043384 .020177 .009452 

81 041716 .019216 .008917 

82 040111 .018301 .008412 

83 038569 .017430 .007936 

84 037085 .016600 .007487 

85 035659 .015809 .007063 

86 034287 . 015056 . 006663 

87 032969 .014339 .006286 

88 031701 .013657 .005930 

89 030481 .013006 .005595 

90 029309 .012387 .00527S 

91 028182 .011797 .004979 

92 027098 .011235 .004697 

93 026056 .010700 .004432 

94 025053 .010191 .004181 

95 024090 .009705 .003944 

96 023163 .009243 .003721 

97 022272 .008803 .003510 

98 021416 . 008384 . 003312 

99 020592 .007985 .003124 

100 019S00 . 007604 . 002947 

101 019038 .007242 .002780 

102 018306 .006897 .002623 

103 017602 . 006569 . 002474 

104 016925 .006256 .002334 

105 016274 .005958 .002202 



FORCE OP MORTALITY TABLE. 



87 



Table III. 
Force of Mortality. 



Makehamlzed 
Ahebican. 

Age. » A'x 

10 .00768 

11 .00769 

12 .00770 

13 .0077^ 

14 .00773 

15 .00775 

16 .00776 

17 .00775 

18 .0075i 

19 .00183 

20 .00756 

21 .00788 

22 .0079^ 

23 .00795 

24 .00799 

25 .00504 

26 .00809 

27 .005J4 

28 .00821 

29 .005^7 

30 .00835 

31 .008Jf3 

32 .00555 

33 . 00863 

34 .00876 

35 .00555 

36 .00902 

37 .00918 

38 .00955 

39 .00955 

40 .00977 

41. .0J007 



Mafcebamlzed 
Cablisle. 



.00507 

.00519 

.00533 

.00548 

.00565 

.00583 

.00602 

.00624 

.00648 

.00674 

.00702 

.00733 

,00767 

.00804 

.00894 

.00902 

.00910 

.00920 

.00930 

.00942 

.00955 

.00968 

.00983 

.01000 

.01018 

.01038 

.01060 

.01083 

.01100 

.01137 

.01168 



88 



FOECE OF MOBTALITY TABIiB. 



Table m — {Continued). 



Age. 

42. 
43. 
44. 
45. 
46. 
47. 
48. 
49. 
50. 
51. 
52. 
53. 
54. 
55. 
56. 
57. 
58. 
59. 
60. 
61. 
62. 
63. 
64. 
65. 
66. 
67. 
68. 
69. 
70. 
71. 
72. 
73. 
74. 
75. 
76. 



Makehamlzed 


Makehamlzed 


AUEBICiLN. 


Cablislb. 


/^^ 


/<x 


.01028 


.01202 


.01058 


.01239 


.01091 


.01280 


.01128 


.01324 


.01169 


.01373 


.01215 


.01426 


.01265 


.01484 


.01321 


.01548 


.0138^ 


.01618 


.01453 


.01694 


.01531 


.01778 


.01617 


.01870 


.01712 


.01970 


.01818 


.02079 


.01936 


.02199 


.02066 


.02331 


.02212 


.02475 


.02373 


.02632 


.02553 


.02804 


.02752 


.02993 


.02974 


.03199 


.03220 


.03425 


.03494 


.03672 


. 03798 


.03942 


.04136 


.04238 


.04512 


.04562 


.04929 


.04917 


.05393 


.05305 


.05908 


.05730 


.06481 


.06195 


.07117 


.06703 


.07824 


.07260 


.08610 


.07870 


.■0948S 


.08537 


.10453 


.09267 



FOECE OF MORTALITY TABLE. 



89 



Table III — {Concluded'). 



Age. 

n. 

Y8. 

79. 

80. 

81. 

82. 

83. 

84. 

85. 

86. 

87. 

88. 

89. 

90. 

91. 

92. 

93. 

94. 

95. 

96. 

97. 

98. 

99. 
100. 
101. 
102. 
103. 
104. 
106. 



Makehamized 
American. 


Makehamlsed 
Caklisle. 


Mx 


M^ 


.11531 


.10066 


. 12729 


.10941 


.14060 


.11898 


.15340 


.12945 


.17183 


.14092 


.19010 


.15347 


.21040 


.16720 


.23295 


.18223 


. 25801 


.19869 


.28586 


.21669 


.31681 


.23640 


.35120 


.25797 


.38941 


.28158 


.43187 


.30742 


.47905 


.33569 


.53149 


.36665 


.58975 


.40053 


.65449 


.43760 


. 72643 


.47818 


.80637 


.52258 


.89521 


. 57'120 


.99392 


. 62440 




.68262 




.74635 




.81611 




.89243 




.97599 




1.06742 




1.16751 



90 NOETHAMPTON EXPBEIBNCE TASLBS. 



Table IV. 
HOETHAMPTON Table of Mortality. 

; J Expec- 

Age. '» •" tation. 

11,650 3,000 25.18 

1 8,650 1,367 32.74 

2 7,283 502 37.79 

3 6,781 335 39.55 

4 6,446 197 40.58 

5 6,249 184 40.84 

6 6,065 140 41.07 

7 5,925 110 41.03 

8 5,815 80 40.79 

9 5,735 60 40.36 

10 5,675 52 39.78 

11 5,623 50 39.14 

12 5,573 50 38.49 

13 5,523 50 37.83 

14 5,473 50 37.17 

15 5,423 50 36.51 

16 5,373 53 35.85 

17 5,320 58 35.20 

18 5,262 63 34.58 

19 5,199 67 33.99 

■20 5,132 72 33.43 

21 5,060 75 32.90 

22 4,985 75 32.39 

23 4,910 75 31.88 

24 4,835 75 31.30 

25 4,760 75 30.85 

'36 4,685 75 30.33 

-27 4,610 75 29.82 

28 4,536 75 29.30 

29 4,460 75 28.79 

30 4,385 75 28.27 

31 4,310 75 27.76 

32 4,235 75 27.24 

33 4,160 75 26.72 



NORTHAMPTON MOETALITY TAJBUB. 91 



Expec- 
tation. 



Table IV — (Continued). 

Age. Ix dx 

34 4,085 75 26.20 

35 4,010 75 25.68 

36 3,935 75 25.16 

37 3,860 " 75 24.64 

38 3,785 75 24.12 

39 3,710 75 23.60 

40 3,635 76 23.08 

41 3,559 77 22.56 

42 3,482 78 22.04 

43 3,404 78 21.54 

44 3,326 78 21.03 

45 3,248 78 20.52 

46 3,170 78 20.02 

47 3,092 78 19.51 

48 3,014 78 19.00 

49 2,936 79 18.49 

50 2,857 81 17.99 

51 2,776 82 17.50 

52 2,694 82 17.02 

53 ' 2,612 82 16.54 

54 2,530 82 16.06 

55 2,448 82 15.58 

56 2,366 82 15.10 

57 2,284 82 14.63 

58 2,202 82 14.15 

59 2,120 82 13.68 

60 2,038 82 13.21 

61 1,956 82 12.75 

62 1,874- 81 12.28 

63 1,793 81 11.81 

64 1,712 80 11.35 

65 1,632 80 10.88 

66 1,552 80 10.42 

67 1,472 80 9.96 

68 1,392 80 9.50 

69 1,312 80 9.05 



92 NORTHAMPTON EXPEBIENCE TABLES. 

Table IV — (Concluded). 

, , Expec- 

Age. 'a; "'X tation. 

70 1,232 80 8.60 

71 1,152 80 8.17 

72 1,072 80 7.74 

73 992 80 7.33 

74 912 80 6.92 

75 , 832 80 6.54 

76 752 77 6.18 

77 675 73 5.83 

78 602 68 5.48 

79 534 65 5.11 

80 469 63 4.75 

81 406 60 4.41, 

82 346 57 4.09 

83 289 55 3.80 

84 234 48 3.58 

85 186 41 3.37 

86 145 34 3.19 

87 Ill 28 3.01 

88 83 21 2.86 

89 62 16 2.66 

90 46 12 2--1 

91 34 10 2.0!) 

92 24 8 1.75 

93 16 7 r.37 

94 9 3 1.05 

95 4 3 .75 

96 1 1 .50 



SINGLE LIFE — ANNUITIES — SINGLE PREMIUMS. 93 



Table V — Single Life. 

ANNUITIES AND SINGLE PREMIUMS PER $1. 

NORTHAMPTON Table of Mortality, tvith Interest 
at 5/^ Per Annum. 

Single 

Age. Annuity. Premium. 

10 15.139 .23148 

11 15.043 .23605 

12 14.937 .24110 

13 14.826 .24638 

14 14.710 .25191 

15 14.588 .25771 

.16 14.460 .26381 

17 14.334 .26981 

18 14.217 .27538 

19 , 14.108 .28057 

20 14.007 .28538 

21 13.917 .28967 

22 13.833 .29367 

23 13.746 .29781 

24 13.658 ,30200 

25 13.567 .30633 

26 13.473 .31081 

27 13.377 ,31538 

28 13.278 .32010 

29 13.177 .32491 

30 13.072 .32991 

31 12.965 .33500 

32 , 12.854 .34029 

33 12.740 .34571 

34 12.623 .35129 

35 12.502 .35705 

36 12.377 .36300 

37 12.249 .36910 

38 12.116 .37543 

39 11.979 .38195 

40 11.837 .38871 



94 



NOBTHAMPTON EXPERIENCE TABLES. 



Table V — (Continued). 

Blngle 

Age. Annuity. Premium. 

41 11.695 .39548 

42 11.551 .40233 

43 11.407 .40919 

44 11.258 .41629 

45 11.105 .42357 

46 10.947 .43110 

47 10.784 .43886 

48 10.616 .44686 

49 10.443 .45510 

50 10.269 .46338 

51 -. ... 10.097 .47157 

52 9.925 .47976 

53 9.748 .48819 

54 9.567 .49681 

55 9.382 .50562 

56 9.193 .51462 

57 8.999 .52386 

58 8.801 .53329 

59 8.599 .54291 

60 - 8.392 .55276 

61 8.181 .56281 

62 7.966 .57305 

63 7.742 .58371 

64 7.514 .59457 

65 *.. 7.276 .60591 

66 7.034 .61743 

67 6.787 .62919 

68 6.536 .64114 

69 6.281 .65329 

70 6.023 .66557 

71 5.764 .67791 

72 5.504 • .69029 

73 5.245 .70262 

74 4.990 .71476 

75 4.744 .72648 

76 4.511 .73757 



8IN6IiB 


LIFE — ANNUITIES — SINGLE PBBMIUMS. 95 




Table V — {Concluded). 


single 


Age. 


Annuity. 


Premium. 


11.... 


4.277 


.74871 


78.:.., 


4.035 


■ .76024 


79.... 


3.776 


.77257 


80.... 


3.515 


.78500 


81.... 


3.263 


.79700 


82.... 


3.020 


.80857 


83 


2.797 


.81919 


84 


2.627 


.82729 


85 


2.471 


.83473 


86 


2.328 


.84152 


87.... 


2.193 


.84795 


88 


2.080 


.85333 


89.... 


1.924 


.86076 


90.... 


1.723 


.87033 


91 


1.447 


.88348 


92.... 


1.153 


.89748 


93.... 


.816 


.91353 


94 


.524 


.92743 


95 


.238 


. 94105 



N. B. — The column headed "Annuity " in the above 
table is the one which is used in the calculation of life 
estates and dower rights. The column headed " Single 
Premium " is tha one which is used in the calculation of 
the present value of remainders. 



96 



NORTHAMPTON EXPERIENCE TABLES. 



Table VI — Two Lives. 

ANNUITIES AND SINGLE PREMIUMS PER $1. 

NORTHAMPTON Table of Mortality, with Interest 
at 5^ Per Annum. 

order. Younger. Annuity. Premium. 

10 10 12.665 .34£r2S 

11 11 12.546 .35495 

12 12 12.411 .36138 

13 13 12.268 .36819 

14 14 12.118 .37533 

15 10 12.302 .36657 

15 11.960 .38286 

le 11 12.158 .37343 

16 11.793 .39081 

17 12 12.009 .38052 

17 11.630 .39857 

18 13 11.864 .38743 

18 11.483 .40557 

19 14 11.723 .39415 

19 11.351 .41185 

20 10 11.906 .38542 

15 11.585 .40071 

20 11.232 .41752 

21 11 •. . 11.797 .39062 

16 11.452 .40704 

21 11.131 .42233 

22 12 11.686 .39590 

17 11.327 .41300 

22 11.042 .42657 

23 13 1,1.570 .40143 

18 11.209 .41862 

23 i0.951 .43090 

24 14 11.450 .40714 

19 11.096 .42400 

24 10.858 .43533 

25 10 11.627 .39872 



TWO LIVES ANNUITIES SINGLE PREMIUMS. 97 



Older. 


Table VI — 

AOBS. 

Younger. 


■ (Continued). 

Annuity. 


Single 
Premium. 


25 


15 


11.324 


.41314 




20 


10.989 


.42909 




25 


10.764 


.43981 


26 


11 


11.519 


.40386 




16 


11.193 


.41938 




21 


10.890 


.43381 




26 


10.667 


.44443 


27 


12 


11.402 


.40942 




17 


11.063 


.42557 




22 


10.796 


.43828 




27 


10.567 


.44919 


28 


13 


11.280 


.41524 




18 


10.939 


.43147 




23 


10.699 


.44290 




28 


10.466 


.45400 


29 > 


14: 


11.153 


.42129 




19 


10.820 


.43714 




24 


10.600 


.44762 




29 


10.362 


.45895 


30 


10 


11.304 


.41410 




15 


11.021 


.42757 




20 ' 


10.707 


.44253 




25 


10.499 


.45243 




30 


10.255 


.46405 


31 


11 


11.188 


.41962 




16 


10.883 


.43415 




21 


10.600 


.44762 




26 .'.. 


10.396 


.45733 




31 


10.146 


.46923 


32 


12 


ii.oe2 


.42561 




17 


10.746 


.44066 




22 


10.498 


.45248 




27 


10.289 


.46243 




32 


10.034 


.47457 


33 


13 


10.932 


.43180 




18 


10.613 


.44700 




7 







98 



NOKTHAMPTON EXPERIENCE TABLES. 





Table VI — 


■ (Continued). 


\ 


Older. 


Ages. 

Younger. 


Annuity. 


Single 
Premium. 


33 


23 


10.393 


.45748 




28 


10 . 181 


.46757 




33 


9.919 


.48005 


34 


14 


10.796 


.43828 




19 


10.486 


.45304 




24 


10.285 


.46262 




29 


10.069 


.47290 




34 


9.801 


.48566 


35 


10 


10.916 


.43257 




15 


10.655 


.44500 




20 


10.363 


.45891 




25 


10.175 


.46786 




30 


9 . 954 


.47838 




35 


9.680 


.49143 


36 


11 


10.788 


.43867 




16 


10.507 


.45205 




21 


10.246 


.46447 




26 


10.062 


.47323 




31 


9.837 


.48396 




36 


9.555 


.49738 


37 


12 


10.651 


.44519 




17 


10.35& 


.45914 




22 


10.132 


.46990 




27 


9.946 


.47876 




32 


9.716 


.48971 




37 


9.427 


.50348 


38 


13 


10.509 


.45195 




18 


10.214 


.46600 




■ 23 


10.015 


.47547 




28 


9.826 


.48447 




33 


9.591 


.49566 




38 


9.294 


.50981 


39 


14 


10.360 


.45905 




19 


10.074 


.47267 




24 


9.895 


.48119 




29 


9.703 


.49034 



TWO LIVES ANNUITIES SINGLE PEEMIUIIS. 99 



Table VI — (Continued). 

Ages. Single 

Older. Younger. Annuity. Premium. 

39 34... 9.463 .50176 

39 ; 9.158 .51629 

40 10 10.442 .45514 

15 10.205 .46643 

20 9.937 .47919 

25 9.771 .48709 

30 9.576 .49638 

35 9.331 .50805 

40 9.016 .52304 

41 11 10.302 .46180 

16 10.046 .47400 

21 9.809 .48528- 

26 9.647 .49300 

ai 9.448 .50248 

36 9.198 .51438 

41 8.876 .52971 

42 12 10.156 .46876 

17 9.889 .48147 

22 9.685 .40119 

27 9.522 .49895 

32 9.320 .50857 

37 9.062 .52085 

42 8.737 .53634 

43 13 10.007 .47580 

18 9.739 .48862 

23 9.562 .49704 

28 9.396 .5049.> 

33 9.190 .5147© 

38 8.927 .52729 

43 8.599 .54290 

44 14 9.852 .48323 

19 9.592 .49561 

24 9.435 .50309 

20 9.267 .51110 

34 9.058 .52105 

39 8. .787 .53396 



100 



NOBTHAMPTON EXPEBIENCE TABLES. 



Table VI — 


■ (Continued). 




AGES. 

Older. Younger. 


Annuity. 


Single 
Premium. 


44 44 


8.457 


.54967 


45 10 


9.900 


.48095 


15 


9.690 


.49095 


20 


9.448 


.50248 


25 


9.304 


.50933 


30 


9.135 


. 5173& 


35 


8.921 


.52757 


40 


8 . 643 


.54081 


45 


8.312 


.55657 


46 11 


9.774 


.48695 


16 


9.522 


.49895 


21 


9.310 


.50905 


26 


9.170 


.51571 


31 


8.998 


.52391 


36 


8.781 


.53424 


41 


8.497 


.54777 


46 


8.162 


.56371 


47 12 


9.592 


.49561 


17 


9.353 


.50700 


22 


9.173 


.51557 


27 


9.032 


.52228 


32 


8.858 


.53057 


37 


8.636 


.54114 


42 


8.350 


.55476 


47 


8.008 


.57105 


48 13 


9.425 


.50357 


18 


9.186 


.51495 


23 


9.031 


.52233 


28 


8.890 


.52905 


33 


8.714 


.53743 


38 


8.487 


.54824 


43 


8.200 


.56190 


48 


7 . 849 


.57862 


49 14 


9.252 


.51180 


19 


9.021 


.52281 


24 


8.886 


.52923 



TWO 


LIVES ANNUITIES 


— SINGLE PREMIUMS. 101 




Table VI — 


(Continued). 




Older. 


Ages. 

Younger. 


Annuity. 


single 
Premium. 


49 


29 


8.744 


.53600 




34 


8.565 


.54452 




39 


8.333 


.55557 




44 


8.046 


,56923 




49 


7.686 


.58638 


50 


10 


9.260 


.51143 




15 


9.076 


.52019 




20 


8.861 


.53043 




25 


8.739 


.53624 




30 


8.596 


.54304 




35 


8.415 


.55166 




40 


8.177 


.56300 




45 


7.891 


.57662 




50 


7.522 


.59419 


51 


11 


9.100 


.51905 




16 


8.899 


.52862 




21 


8.712 


,53752 




26 


&.595 


.54309 




31 


8.451 


.54995 




36 


8.267 


.55872 




41 


8.025 


.57024 




46 


7.737 


.58396 




51 


7.366 


.60161 


52 


12 


8.934 


.52695 




17 


8.724 


.53695 




22 


8.568 


.54438 




a? 


8.451 


.54995 




32 


8.306 


.55685 




37 


8.119 


.56576 




42 


7.875 


.57738 




47 


7.582 


.59133 




52 


7.213 


.60891 


53 


13 


8.763 


.53510 




18 


8.552 


.54514 




23 


8.421 


.55138 




28 


8.304 


.55695 



102 



. NOETHAMPTON EXPERIENCE TABLES. 



Table VT — {Continued). 

Ages. Single 

Older. Younger. Annuity. Premium. 

53 33 8.157 .56396 

ys 7.966 .57304 

43 7.724 .58457 

48 7.424 .59886 

53 7.056 .61638 

54 14 , 8.586 .54352! 

19 8.383 .55319 

24 8.270 .55857 

20 8.153 . .56415 

34 8.005 .57119 

39 7.810 .58048 

44 7.569 .59195 

49 7.262 .60657 

54 6.897 .62396 

55 10 8.560 .54476 

15 8.403 .55224 

20 8.216 .56114 

2.3 8.116 .56590 

30 7.999 .57147 

■?,:, 7.849 .57862 

40 7.651 .58805 

4.-, 7.411 .59947 

50 7.098 .61438 

55 6.73.? .63166 

56 11 8.386 .55304 

16 8.214 .56124 

21 8.053 . .56891 

26 7.958 .57343 

31 7.841 .57900 

36 7.690 .5861!) 

41 7.489 .59576 

40 7.249 .0071!) 

• 51 6.936 .62209 

56 6.571 .63947 

57 12 S.203 .56176 

17 ^^.024 .57029 



TWO LIVES ANNUITIES 


— SINGLE PREMIUMS. lOd 


Table VI — 


(Continued). 




AGES. 
Older. Younger. 


Annuity. 


Single 
Premium. 


57 22 


7.891 


.57662 


27 


7.797 


.58110 


32 


7.680 


.586(17 


37 


7.527 


.59396 


4:2 


7.326 


.60352 


47 


7.084 


.61505 


52 


6.774 


.62981 


57 


6.404 


.64743 


58 13 


8.015 


.57071 


18 


7.835 


.57928 


23 


7.725 


.58452 


28 


7.632 


.58895 


33 


7.515 


.59452 


38 


7.360 


.60190 


43 


7.162 


.61133 


48 


6.915 


.62309 


53 


6.609 


.63767 


58 


6.234 


.65552 


59 14 


7.821 


.57995 


19 


7.648 


.58819 


24 


7.556 


.59257 


29 


7.464 


.59695 


34 


7.346 


.60257 


39 


7.189 


.61005 


44 


6.994 


.61933 


49 


6.742 


.63133 


54 


6.442 


.64561 


59 


6.062 


.66371 


60 10 


7.750 


.58333 


15 


7.622 


.58942 


20 


7.463 


.59700 


25 


7.383 


.60081 


30 


7.292 


.60514 


35 


7.174 


.61076 


40 


7.015 


.61833 


45 


6.822 


.62752 



104 



NORTHAMPTON EXPEKIENCE TABLES. 



Older. 
60 



61 



62 



63 



Table VI — (Continued). 

Ages. Single 

Younger. Annuity. Premium. 

50 6.568 .63962 

55 '. . 6.272 .65371 

60 5.888 .67200 

11 7.557 .59253 

16 7.416 .59923 

21 7.281 .6056& 

26 7.207 .60919 

31 7.116 .61352 

36 fi.998 .61914 

41 6.838 .62676 

46 6.648 .63581 

51 6.395 .64786 

56 6.100 .66190 

61 5.712 .68038 

12 7.357 .60205 

17 7.208 .60914 

22 7.100 .61429 

27 7.027 .61777 

32 6.937 .62205 

37 6.819 .62767 

42 6.660 .63524 

47 6.469 .64433 

52 6.222 .65609 

57 5.925 .67024 

62 5.533 .68891 

13 7.147 .61205 

18 6.998 .61914 

23 6.910 .62333 

28 6.839 .62671 

33 6.750 .63095 

38 6.631 .63662 

43 6.477 .64396 

48 6.283 .65319 

53 6.042 .66466 

58 5.744 .67886 

63 5.347 .69777 



TWO LIVES ANlSrUITIES SINGLE PREMIUMS. 105 



Table VI — (Continued). 

Ages. Single 

Older. Younger. Annuity. Premium. 

64 14 6.931 .6223.3 

19 6.789 .62909 

24 6.717 .63253 

29 6.648 .63581 

34 6.559 .64005 

39 6.440 .64571 

44 6.289 .65290 

49 6.093 .66224 

54 5.860 .67333 

59 5.561 .68757 

64 5.158 .70676 

€5 10 6.803 .62843 

15 6.705 .63309 

20 6.576 .63923 

25 6.515 .64214 

30 6.447 .64538 

35 6.360 .64952 

40 6.240 .65524 

45 6.094 .66219 

50 5.897 .67157 

55 5.671 .68233 

60 5.372 .69657 

65 4.960 .71619 

66 11 6.581 .63900 

16 6.472 .64419 

21 6.364 .64933 

26 6.309 .65195 

31 6.243 .65510 

36 6.156 .65923 

41 6.037 .66491 

46 5.894 .67171 

51 5.701 .68090 

56 5.479 .69147 

61 ■■ 5.180 .70571 

66 4.759 .72576 

67 12 6.351 .64995 



106 



NORTHAMPTON EXPERIENCE TABLES. 



Table VI- 


- (Continued). 




Ages. 
Older. Younger. 


Annuity. 


Single 
Premium. 


67 17 


6.236 


.65542 


00 


6.151 


.65947 


27 


6.098 


.66200 


32 


6.033 


. 66510 


37 


5.948 


.66914 


42 


5.831 


.67471 


47 


5.690 


.68143 


52 


5 . 504 


.69029 


57 


5.283 


.70081 


62 


4.986 


.71495 


67 


4.555 


.73547 


68 13 


6.116 


.66114 


18 


6.001 


.66662 


23 


5.934 


.66981 


28 


5.883 


.67224 


33 


5.820 


.6752+ 


38 


5.735 


.67928 


43 


5.622 


.68466 


48 


5.481 


.69138 


53 


5.303 


.6998o 


58 


5.084 


.71029 


63 


4.786 


.72447 


68 


4.348 


.74533 


69 14 


5.876 


.67257 


19 


5.766 


.67781 


24 


5.713 


.68034 


29 


5.664 


.68267 


34 


5 . 603 


.68557 


39 


5.518 


.68962 


44 


5.411 


.69471 


49 


5.268 


.70152 


54 


5 . 100 


.70952 


59 


4.883 


.71986 


64 


4.585 


.73405 


69 


4.140 


.75524 


■70 10 


5.700 


.68095 



TWO LIVES ANNUITIES SINGLE PREMIUMS. 107 



Table VI — {Continued). 

Older. Younger. Annuity. 

TO 15 5.631 

20 5.532 

25 5.489 

30 5.442 

35 5.382 

40 5.298 

45 5.195 

50 5.054 

55 4.893 

60 4.680 

65 4.378 

70 3.930 

71 11 • 5.460 

16 5.382 

21 5.300 

26 5.263 

31 ., 5.218 

36 .' 5.159 

41 5.076 

46 4.978 

51 4.841 

56 4.685 

61 4.476 

66 . 4.169 

71 3.719 

72 12 5.216 

17 5.133 

22 5.070 

27 5.035 

32 4.992 

37 4.934 

42 4.854 

47 4.758 

52 4.630 

57 4.477 

62 4.272 



Single 
Premium. 

. GS42'4 
.68895 
.69100 
.693l>:^ 
.0960'9 
.70010 
.70500 
.71171 
.71938 
.72952 
.74391 
.76524 
.692r.8 
.69609 
.70000 
.70176 
.70391 
.■70671 
.71066 
.71533 
.72185 
. 7202S 
.73923 
.7538-6 
.77528 
. 70400 
.70796 
.71095 
.712G2 
.71466 
.71743 
.72124 
72581 
73190 
.73919 
.74895 



108 



NOKTHAMPTON EXPERIENCE TABLES. 





Table VI — 


• (Continued). 




Older. 


Ages. 

Younger. 


Annuity. 


. Single 
Premium. 


72 


67 


3.960 


.76381 




72 


3.510 


.78524 


73 


13 


4.972 


.71561 




18 


4.889 


.71957 




23 


4.841 


.72185 




28 


4.808 


.72343 




33 


4.766 


.72542 




38 


4.710 


.72810 




43 


4.634 


.73171 




48 


4.539 


.73624 




53 


4.417 


.74205 




58 


4.269 


.74909 




63 


4.066 


.75876 




6& 


3.752 


.77371 




73 


3.304 


.79505. 


74 


14 


4.731 


.72709 




19 


4.651 


.73090 




24 


4.615 


.73262 




29 


4.583 


.73415 




34 


4.543 


.73605 




39 


4.488 


.73867 




44 


4.417 


.74205 




49 


4.322 


.74657 




54 


4.208 


.75200 




59 


4.064 


.75886 




64 


3.864 


.76838 




69 


3.547 


.78348 




74 


3.105 


.80452 


75 


10 


4.522 


.73704 




15 


4.495 


.73833 




20 


4.424 


.74171 




25 


4.396 


.74304 




30 


4.365 


.74452 




35 


4.327 


.74634 




40 


4.272 


.74895 




45 


4.206 


.75209 



TWO 


LIVES ANNUITIES • 


— SINGLE PREMIUMS. 109 




Table VI — 


(Continued). 






Ages. 




single 
Premium. 


Older. 


Younger. 


Annuity. 


75 


50 


4.112 


.75657 




55 


4.006 


.76161 




60 


3.860 


.76828 




65 


3.665 


.77786 




70 


3.347 


.79300 




75 


2.917 


.81348- 


76 


11 


4.301 


.74757 




16 


4.270 


.74905 




21 


4.212 


.75180 




26 ,. 


4.188 


.75295 




31 


4.160 


.75429 




36 


4.123 


.75605 




41 


4.069 


.75862 




46 


4.006 


.76161 




51 


3.916 


.76590 




56 


3.815 


.77071 




61 


3.679 


.77719 




66 


3.477 


.78681 




71 


3.159 


.80195 




76 


- 2.750 


.82143 


77 


12 


4.195 


.75262 




17 


4.045 


.75976 




22 


4.001 


.76185 




27 


3.979 


.76290 




32 


3.952 


.76419 




37 


3.916 


.76590 




42 


3.865 


.76833 




47 


3.805 


.77119 




52 


3.720 


.77524 




57 


3.623 


.77986 




62 


3.492 


.78609 




67 


3.289 


.79576 




72 


2.971 


.81090- 




77 


2.583 


.82938 


7S 


13 


3.871 


.76805 




18 


3.815 


.77071 



iio 



NOETHAMPTON EXPERIENCE TABLES: 



Table VI — (Continued). 

Ages. Single 

Older. Younger. . Annuity. Premium. 

78 23 3.783 .7722i 

28 3.762 .77323 

33 3.737 .77443 

38 3.702 .77609 

43 3.655 .77833 

48 3.596 .78114 

53 3.518 .78486 

58 3.424 .78933 

(;3 3.297 .79538 

68 3.095 .80500 

73 2.780 .82000 

78 2.410 .83762 

79 14 3.624 .77981 

19 3.571 .78233 

24 3.548 .78343 

29 3.528 .78438 

34 3.505 .78547 

39 3.471 .78709 

44 3.428 .78914 

49 3.369 .79195 

54 3.299 .79528 

59.. 3.210 .79952 

64 3.088 .80533 

69 2. 887 .81419 

74 2.580 .82952 

79 2.217 .84681 

80 10 3.395 .79071 

15 3.372 .79180 

20 3.325 .79405 

25 3.308 .79486 

30 3.290 .79571 

35 3.268 .79676 

40 3.236 .79828 

45 3.197 .80015 

, 50 3.140 .80286 

55 3.076 .80590 



TWO LIVES ANNUITIES SINGLE PREMIUMS. Ill 



Table VI — {Continued). 

Ages. Single 

Older. Younger. Annuity. Premium. 

80 GO 2.992 .80990 

65 2.873 .81557 

70 2.675 .82500 

75 2.381 .83900 

80 2.018 .85629 

81 11... 3.156 .80209 

16 ' 3.128 .80343 

21 3.091 .80519 

26 3.077 .80586 

31 3.060 .80667 

36 3.040 .80762 

41 3.009 .80909 

46 2.973 .81081 

51 2. .920 .81333 

56 2.861 .81614 

61 2.782 .81990 

66 , 2.664 .82552 

71 2.470 .83476 

76 2.195 .84786 

81 1.-827 .86538 

82 12 2.924 .81314 

17 2.893 .81462 

22 2.865 .81595 

27 2.853 .81653 

32 2.838 .81724 

37 2.818 .81819 

42 2.789 .81957 

47 2.756 .82114 

53 2.70^7 .82348 

57 2.651 .82614 

62 2.578 .82962 

67 2.461 .83519 

72 2.271 .84424 

77 2.013 .85653 

82 1.642 .87419 

83 13 2.709 .82338 



112 



NORTHAMPTON EXPERIENCE TABLES. 



Table VI — 


■ (Continued). 




Agss. 




Single 


Older. Younger. 


Annuity. 


Premium. 


83 18 


2.677 


.82491 


23 


2.657 


.82586 


28 


2.646 


.82638 


33 


2.632 


. 82704 


38 


2.613 


.82796 


43 


2.587 


.82919 


48 


2.554 


.83076 


53 


2.510 


.83286 


58 


2.457 


.83538 


63 


2.387 


.83872 


68 


2.272 


.84419 


73 


2.085 


.85309 


78 


1.838 


.86486 


83 


1.472 


.88228 


84 14 


2.545 


.83119 


19 


2.513 


.83272 


24 


2.499 


.83338 


29 


2.489 


.83386 


34 


2.476 


.83447 


39 


2.457 


.83538 


44 


2.433 


.83653 


49 


2.400 


;83810 


54 


2.360 


. 84000 


59 


2.310 


.84238 


64 


2.242 


.84561 


69 


2.126 


.85114 


74 


1 . 941 


.85995 


79 


1.750 


.86905 


84 


1.357 


.88777 


85 15 


2.393 


.8-3843 


20 


2.364 


.83981 


25 


... ' 2.354 


.84029 


30 


2.344 


.84076 


35 


2.331 


.84138 


40 


2.313 


.84224 


45 


2.291 


.84328 



TWO LIVES ANNUITIES SINGLE PKEMIUMS. 113 

Table VI — (Continued). 

Aqbs. single 

Older. Younger. Annuity. Premium. 

85 50 2.258 .84486 

55 . 2.222 .84657 

60 2.174 .84886 

65 2.107 .85205 

70 ' 1.991 .85757 

75 1.811 .86614 

80 1.573 .87748 

85 1.256 .89257 

86 16 2.253 .84510 

21., 2.229 .84624 

26 2.221 .84662 

31 2.212 .84704 

36 2.200 .84762 

41 2.182 .84847 

46 2.162 .84942 

51 2.131 .85090 

56 2.097 .85253 

61 2.051 .85471 

66 1.984 .85791 

71 1.867 .86348 

76 1.699 .87147 

81 1.447 .88348 

86 1.171 .89662 

87 17 2.121 .85138 

22 2.104 .85219 

27 2.096 .85257 

32 2.088 .85295 

37 2.077 .85348 

42 2.060 .85429 

47 2.041 .85519 

52 2.012 .85657 ' 

57 1.980 .85810 

62 1.937 .86015 

67 1.870 .86333 

72 1.753 .86891 

77 1.597 .87634 



114 NORTHAMPTON EXPERIENCE TABLES. 

Table VI — (Continued). 

Older. Younger. Annuity. Premium. 

87 82 1 . 329 . 88909 

87 1.098 .90010 

88 18 2.012 .85657 

23 1.999 .85719 

28 1.992 .85752 

33 1.985 .85786 

38 1.974 .85838 

43 1.959 .85909 

48 1.941 .85995 

53 1.914 .86124 

58 1.883 .86272 

63 1.843 .86462 

68 1.777 .86777 

73 1.660 .87333 

78 1.514 .88029 

83 1.235 .89357 

88 1.063 .90176 

89 19 1.862 .86371 

24 1.854 .86410 

29 1.848 .86438 

34 1.841 .86471 

39 1.832 .86514 

44 1.818 .86581 

49 1.800 .86667 

54 1.778 .86772 

59 1.750 .86905 

64 1.714 .87076 

69 1.650 .87381 

74 1.538 .87914 

79 1.400 .88571 

84 1.145 .89786 

89 1.001 .90471 

90 20 1.670 .87286 

25 -. 1.665 .87309 

30 1.660 .87333 

35 1.654 .87362 



TWO LIVES ■ 



ANNUITIES ■ 



■ SINGLE PREMIUMS. 



115 



Table VI — (Continued). 

Ages. ' Single 

Older. Younger. Annuity. Premium. 

90 40 1.646 .87400 

45 1.635 .87452 

50 1.619 .87528 

55 1.601 .87614 

60 1.577 .87729 

65 1.544 .87886 

70 1.486 .88161 

75 1.387 .88634 

80 1.255 .89262 

&5 1.038 .90295 

90 .909 .90909 

91 21 1.407 .88538 

26 1.404 .88552 

31 1.400 .88571 

36 1.395 .88595 

41 1.388 .88629 

46 1.380 .&8667 

51 1.367 .88729 

56 1.353 .88796 

61 1.334 .88886 

66 1.307 .89015 

71 1.259 .89243 

76 1.180 .89619 

81 1.061 .90185 

8.6 .892 .90990 

91 . .748 .91676 

92 22 1.124 .89886 

27 1.122 .89895 

32 1.119 .89909 

37.: 1.116 .8992n 

42 1.111 .89947 

47 1.105 .89970 

52 1.095 .90024 

57 1.085 .90071 

62 1.071 .90138 

67 1.050 .90238 



116 NORTHAMPTON EXPERIENCE TABLES. 

Table VI — (Continued). 

Ages. Single 

Older. Younger. Annuity. Premium. 

92 72 1.012 .90419 

77 .955 .90690 

82 .852 .91180 

87 .734 .91743 

92 .576 .92495 

93 23 .798 .91438' 

28 .797 .91443 

33 .795 .91452 

38 .793 .91462 

43 .790 .91476 

48 .786 .91495 

53 .780 .91524 

58 .773 .91557 

63 .764 .91600 

68 .750 .91667 

73 .723 .91796 

78 .688 .91962 

83 .606 .92352 

88 .547 .92634 

93 .361 .93519 

94 24 .514 .92791 

29 .513 .92796 

34 .512 .92800 

39 .511 .92805 

44 .509 .92814 

49 .507 .92824 

54 .503 .92843 

,59 .499 .92862 

64 .494 .92886 

69 .485 .92928 

74 .469 .93005 

79 .448 .93105 

84 .398 .93338 

89 .369 .93481 

94 .199 .94290 

95 25 .234 .94124 



TWO LIVES —n ANNUITIES — SINGLE PEEMIUMS. 117 



Table VI — (Concluded). 

Ages. Single 

Older. Younger. Annuity. Premium. 

95 30 .234 .94124 

35 .233 .94129 

40 .233 .94129 

45 .232 .94133 

50 .231 .94138 

55 .230 .94143 

60 .228 .94152 

65 .226 .94161 

70 .222 .94180 

15 .215 .94214 

80 .206 .942.')'7 

85 .185 .94357 

90 .175 .94405 

95 .059 .94957 



118 



NOKTHAMPTON EXPERIENCE TABLES. 



Table VII — Single Life. 

ANNUITIES AND SINGLE PEEMIUMS PEE $1. 

NORTHAMPTON Table of Mortality, 



Age. 

10. 

11. 

12. 
13. 
1-1. 
15. 
16. 
17. 
18. 
19. 
20. 
21. 
22. 
23. 
24. 
25. 
26. 
27. 
28. 
29. 
30. 
31. 
32. 
33. 
34. 
35. 
36. 
37. 
38. 
39. 
40. 



)rtality, 


icitli Interest 


nnmn. 




AnDuity. 


Single 
Premium. 


13.285 


. 19142 


13.212 


.19555 


13.130 


.20019 


13 . 044 


. 20506 


12.953 


.21021 


12.857 


.21564 


12.755 


.22142 


12.655 


.22708 


12.562 


.23234 


12.477 


.23716 


12.398 


.24162 


12.329 


.24553 


12.265 


.24915 


12.200 


.25283 


12.132 


.25668 


12.063 


. 26059 


11.992 


.26461 


11.917 


.26885 


11.841 


.27315 


11.763 


.27757 


11.682 


.28215 


11.598 


.28691 


11.512 


.29177 


11.423 


.29681 


11.331 


.30202 


11.236 


. 30740 


11.137 


.31300 


11.035 


.31877 


10.929 


. 32477 


10.819 


.33100 


10.705 


. 33745 



SINGLE LIFE — ■ ANNUITIES SINGLE PREMIUMS. 119 



Table VII — {Continued). 



Age. 

41. . . 

42 . . ., 

43. .. 

44. .. 

45. . . 

46. .. 
47... 
48... 
49. . . 
50... 
51. .. 
52... 
53. .. 
54... 
55. .. 
56... 
57... 
58... 
59. .. 
60... 
61... 
62... 
63... 
64. .. 
65... 
66... 
67... 
68... 
69... 
70... 
71.^. 
72... 
73... 
74... 
75... 
76... 



Annuity. 

10.589 
10.473 
10.356 
10.235 
10.110 
9.980 
9 . 846 
9.707 
9.563 
9.417 
9.273 
9 . 129 
8.980 
8.827 
8.670 
8.509 
8.343 
8.173 
7.999 
7.820 
7.637 
7.449 
7.253 
7.052 
6.841 
6.625 
6.405 
6.179 
.949 
,716 
.479 
,241 
.004 



5. 
5. 
5. 
5. 
5. 
4.769 



542 
326 



Single 
Premium. 

. 34402 

.35059 

.35721 

. 36400 

.37113 

.37849 

.38608 

.39394 

.40'200 

.41036 

.41851 

.42660 

.43509 

.44375 

.45264 

.46175 

.47115 

.48077 

.49062 

.50075 

.51111' 

.52175 

.53285 

. 54423 

.56617 

.56840 

.58085 

.59364 

.60666 

.61985 

.63326 

.64674 

. 66015 

. 6734.-1 

.68631 

.69853 



120 NOETHAMPTON EXPERIENCE TABLES. 

Table VTI — {Concluded). 

single 

Age. Annuity. Premium. 

77 4.109 .71082 

78 3.884 .72355 

79 3.641 , .73730 

80 3.394 .75128 

81 3.156 .76475 

82 2.926 .77777 

83 2.713 .78983 

84 2.551 .79900 

85 2.402 .80743 

86 2.266 .81513 

87 2.138 .82238 

88 2.031 .82843 

89 1.882 .83687 

90 1.689 .84779 

91 1.422 .86291 

92 1.136 .87909 

93 .806 .89777 

94 .518 .91408 

95 .236 .93004 

N. B. — See foot-note at bottom of table V. 



TWO LIVES ANNUITIES SINGLE PKEMIUMS. 121 



Table VIII — Two Lives. 

ANNUITIES AND SINGLE PREMIUMS PEE $1. 

NORTHAMPTON Table of Mortality, with Interest 
at Qi Per Annum. 

Ages. Single 

Older. Younger. Annuity. Premium. 

10 10 11.345 .30123 

11 11 11.249 .30666 

12 12 11.139 .31289 

13 13 11.023 .31945 

14 14 10.899 .32647 

15 10 11 . 048 . 31804 

15 10.767 .33394 

16 11 10.929 .32477 

16 10.626 .34192 

17 12 10.805 .33180 

17 10.489 .34968 

18 13 10.685 .33859 

18 10.365 .35670 

19 14 10.568 .34521 

19 10.255 .36293 

20 10 10.719 .33666 

15 10.453 .35172 

20 10.156 .36853 

21 11 10.631 .34164 

16 10.342 .35800 

21 10.074 .37317 

22 12 10.541 .34673 

17 10.239 .36383 

22 10.002 .37725 

23 13 10.446 .35211 

18 10.140 .36943 

23 9.928 .38144 

24 ' 14 10.348 .35766 

19 10.048 .37465 

24 9.853 .38568 

25 10 10.497 .34922 



122 



NORTHAMPTON EXPEEIENCE TABLES. 



Older. 

25 



26 



27 



28 



29 



30 



*^1 



32 



33 



Table VIII — (Continued). 

Ages. Single 

Younger. Annuity. Premium. 

15 10.244 .36354 

20 9.960 .37962 

25 9.776 .39004 

11 10.410 .35415 

16 10.135 ■ .36972 

21 9.879 .38421 

26 9.697 .39451 

12 10.314 .35958 

17 10.027 .37583 

22 9.803 .38851 

27 9.616 .39909 

13 10.215 .36519 

18 9.924 .38166 

23 9.724 .39298 

28 9.533 .40379 

14 10.110 .37113 

19 9.826 .38721 

24 9.643 .39757 

29 ' 9.448 .40861 

10 10.239 .36383 

15 10.001 .37730 

20 9.732 .39253 

25 9.561 .40220 

30 9.360 .41358 

11 10.144 .36920 

16 9.886 .38381 

21 9.644 .39751 

26 9.476 .40702 

31 9.270 .41868 

12 10.042 .37499 

17 9.771 .39032 

22 9.561 .4P220 

27 9.389 .41194 

32 9.178 .42389 

13 9.934 .38109 

18 9.660 .39660 



TWO LIVES ANNUITIES — : SINGLfE PEEMItTMS. 123 



Table VIII — (Continued). 

Ages. Single 

Older. Younger. Annuity. Premium. 

33 23 9.474 .40713 

28 9.299 .41704 

33 9.082 .42932 

34 14 9.822 .38744 

19 9.554 .40260 

24 9.386 .41211 

29 9.207 .42224 

34 8.984 .43486 

35 10 9.925 .38161 

15 9.703 .39417 

20 9.451 .40843 

25 9.295 .41727 

30 9.112 .42763 

35 8.883 .44058 

36 11 9.820- .38755 

16 9.579 .40119 

21 9.354 .41392 

26 9.201 .42258 

31 9.014 .43317 

36 8.778 .44653 

37 12 9.707 .39394 

17 9.454 .40826 

22 9.260 .41925 

27 ' 9.105 .42802 

32 8.913 .43889 

37 8.670 ' .45264 

38 13 9-588 .40068 

18 9.333 .41511 

23 9.163 .42474 

28 9.005 .43368 

33 8.808 .44483 

38 8.558 .45898 

39 14 9.464 .40769 

19 9.215 .42180 

24 , 9.063 .43040 

29.. 8.902 .43951 



124 



NOKTHAMPTON EXPERIENCE TABLES. 



Table VIII — (Continued). 

Ages. Single 

Older. Younger. Annuity. Premium. 

39 34 8.701 .45088 

39 8.442 .46555 

40 10 9.537 .40356 

15 9.333 .41511 

20 9.100 .42830 

25 8.960 .43623 

30 8.795 .44557 

35 8.589 .45723 

40 8.322 .47234 

41 11 9.420 .41019 

16 9.198 .42276 

21 8.992 .43442 

26 8.855 .44217 

31 8.688 .45163 

36' 8.476 .46362 

41 8.202 ,47914 

42 12 9.298 .41710 

17 9.065 .43029 

22 8.889 .44024 

27 8.751 .44805 

32 8.580 .45774 

37 8.362 .47003 

42 8.083 .48587 

43 13 9.173 .42417 

18 8.938 .43747 

23 8.785 .44614 

28 8.645 .45406 

33 8.471 .46390 

38 8.246 .47664 

43 7.965 .49255 

44 14 9.042 .43159 

19 8.814 .44459 

24 8.670 .45264 

29 8.536 .46023 

34 8.358 .47030 

39 8.127 .48337 



TWO LIVES ANNUITIES SINGLE PEEMIUMS. 125 



Table VIII — (Continued). 

Aghs. Single 

Older. Younger. Annuity. Premium. 

44: 44 7.843 .49945 

45 10 9.088 .42898 

15 8.905 .43934 

20 8.692 .45140 

25 8.569 .45836 

30 8.424 .46656 

35 8.242 .47687 

40 8.003 .49040 

45 7.718 .50653 

46 11 ' 8.962 .43612 

16 8.762 .44744 

21 8.574 .45807 

26 8.455 .46481 

31 8.309 .47307 

36 8.122 .48366 

41 7.878 .49747 

46 7.589 .51383 

47 12 8.827 .44375 

17 8.617 .45564 

22 8.458 .46464 

27 8.338 .47144 

32 8.189 .47987 

37 7.998 .49068 

42 7.751 .50466 

47 7.455 .52142 

48 13 8.686 .45174 

18. 8.473 .46379 

23 8.338 .47144 

28 8.217 .47828 

33 8.066 .48683 

38 7.870 .49792 

43 7.621 .51202 

48 7.316 .52928 

49 14 8.538 .46012 

19 8.332 .47178 

24 8.214 .47845 



126 



NORTHAMPTON EXPEBIENCE TABLES. 



Table VIII — (Continued). 

Ages. Single 

Older. Younger. Annuity. Premium. 

49 29 8.092 .48536 

34 7.938 .49408 

39 7.737 .50545 

44 7.488 .51955 

49.. 7.173 .53738 

50 10 8.548 .45955 

15... 8.386 .46872 

20 8.195 .47953 

25 8.089 .48553 

30 7.966 .49249 

35 7.809 .50138 

40 7.602 .51310 

45 7.353 .52719 

50 7.030 .54547 

51 11 8.411 .46730 

16 8.234 .47732 

21 8.067 ^ .48677 

26 7.966 .49249 

31 7.841 .49956 

36 7.681 .50862 

41 7.470 .52057 

46 7.219 .53477 

51 6.893 .55323 

52 12 8.270 .47528 

17 8.083 .48587 

22 7.944 .49373 

27 7.842 .49951 

32 7.716 .50664 

37 7.553 .51587 

42 7.340 .52792 

47 7.084 .54241 

52 6.758 .56087 

53 13 8.123 .48360 

18 7.934 .49430 

23 7.818 .50087 

28 7.716 .50664 



TWO LIVES ANNUITIES SINGLE PREMIUMS. 127 



Table VIII — (Continued) . 

Ages. Single 

Older. Younger. Annuity. Premium. . 

53 33 7.588 .51389 

38 7.421 .52334 

43 7.208 .53540 

48 6.945 .55029 

53 6.620 .56868 

54 14 7.970 .49226 

19 7.788 .50257 

24 7.688 .50823 

29 7.586 .51400 

34 7.457 .52130 

39 7.286 .53098 

44 7.073 .54304 

49 ■ 6.802 .55838 

54 6.480 .57660 

55 10 '. 7.951 .49334 

15 7.812 .50121 

20 7.643 .51077 

25 7.555 .51576 

30 7.453 .52153 

35 7.322 .52895 

40 7.146 .53891 

45 ,.. 6.935 .55085 

50 6.658 .56603 

55 " 6.336 .58.475 

•56 11 7.801 .50183 

16 '. 7.648 .51049 

21 7.502 .51876 

26 7.419 .52345 

31.. 7.316 .52928 

36 7.183 .53681 

41 7.005 .54689 

46 6.793 .55889 

51.. 6.515 .57463 

56 6.190 .59302 

57 12 7.643 .51077 

17 7.481 .51994 



128 



NOKTHAMPTON EXPEKIENCE TABLES. 





Table VIII — 


(Continued). 




Older. 


Ages. 

Younger. 


Annuity. 


single 
Premium. 


57 


22 


7.362 


.52668 




27 


7.279 


.53138 




32 


7.175 


.53727 




37 


7.041 


. 54485 




42 


6.862 


.55498 




47 


6.648 


.56710 




52 


6.371 


.58277 




57 


6 . 041 


.60145 


58 


13 


7.479 


.52006 




18 


7.316 


. 52928 




23 


7.218 


.53483 




28 


7.135 


.53953 




33 


7.031 


. 54541 




38 


6.894 


.55317 




43 


6.718 


.56313 




48 


6.498 


.57559 




53 


6.225 


.59104 




58 


5.890 


.61000 


59 


14 


7.310 


.52962 




19 


7.153 


.53851 




24 


7.070 


.54321 




29 


6.988 


.54785 




34 


6.884 


.55373 




39 


6.744 


.56166 




44 


6.570 


.57151 




49 


6.344 


.58430 




54 


6.076 


.59947 




59 


5.735 


.61878 


60 


10 


7.250 


.53302 




15 


7.135 


.53953 




20 


6.990 


. 54774 




25 


6.919 


.55175 




30 


6.837 


.55639 




35 


6.732 


.56234 




40 


6.590 


.57038 




45 


6.418 


.58012 



TWO LIVES ANNUITIES SINGLE PKEMIUMS. 129 



Older. 
60 



«1 



62 



63 



Table VIII — (Continued). 

Ages. Single 

Younger. Annuity. Premium. 

50 6.189 .59307 

55 5.924 .60807 

60 5.579 .62760 

11 7.081 .54258 

16 6.953 .54983 

21 6.830 .55679 

26 6.764 .56052 

31 6.682 .56517 

36 6.577 .57111 

41 6.434 .57920 

46 6.263 .58889 

51 6.035 .60180 

56 5.770 .61679 

61 5.420 .63660 

12 6.905 .55255 

17 6.770 .56019 

22 6.670 .56585 

27 6.605 .56953 

32 6.524 .57411 

37 : 6.418 .58012 

42 6.276 .58815 

47 6.104 .59788 

52 5.880 .61057 

57 5.613 .62568 

62 5.259 .64572 

13 6.719 .56307 

18 6.583 .57077 

23 6.503 .57530 

28 ; 6.439 .57892 

33 6.359 .58345 

38 6.252 .58951 

43 6.112 .59744 

48 5 . 937 . 60734 

53 5.719 .61968 

58 5.450 .63491 

63 5.089 .65534 

9 



130 



NORTHAMPTON EXPERIENCE TABLES. 



Table VIH- 


- (Continued). 




Ages. 




Single 


Older. Younger. 


Annuity. 


Premium. 


64 14 


6.527 


.57394 


19 


6.396 


.58136 


24 


6.331 


.58503 


29 


6.268 


.58861 


34 


6.189 


.59307 


39 


6.081 


.59919 


44 


5 . 944 


.60694 


49 


5.767 


.61696 


54 


5.555 


.62897 


59 


5.284 


. 64430 


64 


4.917 


.66507 


65 10 


6.414 


.58034 


15 


6.325 


.58538 


20 


6.205 


.59217 


25 


6.151 


.59522 


30 


6.089 


.59874 


35..: 


6.010 


.60321 


40 .... : 


5.901 


.60937 


45 


5.769 


.61685 


50 


5.590 


.62698 


55 


5.384 


.63864 


60 


5.112 


. 65404 


65 


4.736 


.67532 


66 11 


6.215 


.59161 


16 


6.115 


.59727 


21 


6.015 


.60293 


26 


5.966 


.60570 


31 


5.905 


.60915 


36 


5.827 


: 61356 


41 


5.718 


, 61974 


46 


5.588 


.62710 


51 


5.412 


.63706 


56 


5.209 


.64855 


61 


4.938 


.66389 


66 


4.551 


.68579 


67 12 


6.009 


.60326 



TWO 


LIVES ANNUITIES - 


— SINGLE PREMIUMS. 131 




Table VIII- 


- (Continued). 




Older. 


Ages. * 
Younger. 


Annuity. 


Single 
Premium. 


61 


17 


5.903 


.60926 




22 


5.824 


.61373 




27 


5.776 


.61645 




32 


5.717 


.61979 




37 


5.639 


.62421 




42 


5.532 


.63027 




47 


5.403 


.63757 




52 


5.233 


. 64719 




57 


5.031 


.65862 




62 


4.760 


.67396 




67 


4.363 


.69643 


68 


13 


5.796 


.61532 




18 


5.689 


.62138 




23 


5.628 


. 62483 




28 


5.581 


.62749 




33 


5.524 


.63071 




38 


5.446 


.63513 




43 


5.343 


.64096 




48 


5.213 


.64833 




53 


5.050 


.6575. 5 




58 


4.849 


.66893 




63 


4.576 


. 68438 




68 


4.171 


. 70730 


69 


14 -. .. 


5.578 


.62766 




19 


5.476 


.63343 




24 


5.427 


.63620 




29 


5.383 


.63870 




34 


5.326 


. 64192 




39 


5 . 249 


. 64628 




44 


5.150 


.65189 




49 


5.019 


.65930 




54 


4.864 


.66807 




59 


4.665 


.67924 




64 


4.390 


.69491 




69 


3.977 


.71828 


YO 


10 


5.418 


.63672 



132 



NOETHAMPTON EXPERIENCE TABLES. 



Table VIII — (Continued). 

Aqes. • Single 

Older. Younger. Annuity. Premium. 

70 ' 15 5.355 .64029 

20 5.262 .64555 

25 5.223 .64775 

30 5.180 .65019 

35 -5.125 .65330 

40 5.047 .65771 

45 4.953 .66304 

50 4.822 .67046 

55 4.674 • .67883 

60 4.478 .68993 

65 4.199 .70572 

70 3.781 .72937 

71 11 5.199 .64911 

16 5.127 .65318 

21 5.050 .65755 

26 5.016 .65947 

31 4.974 .66185 

36 4.920 .66491 

41 4.844 .66920 

46 4.753 .67436 

51 4.626 .68155 

56 4.482 .68970 

61 4.289 .70062 

66 4.005 .71670 

71 3.584 .74052 

72 12 4.976 .66174 

17 4.899 .66609 

22 4.840 .66943 

27 4.807 .67130 

32 4.767 .67356 

37 4.714 .67656 

42 4.640 .68075 

47 4.551 .68579 

52 4.430 .69264 

57 4.289 .70062 

62 4.099 .71138 



TWO 


' LIVES ANNUITIES - 


— SINGLE PREMIUMS. 166 




Table VIII- 


- {Continued). 




Older. 


Aqes. 

Younger. 


Annuity. 


Single 
Premium. 


72 


67 


3.811 


.72768 




72 


3.387 


.75168 


73 


13 


4.751 


. 67447 




18 


4.673 


. 67889 




23 


4,628 


.68144 




28 


4.597 


.68318 




33 


4.559 


.68534 




38 


4.507 


.68828 




43 


4.436 


.69230 




48 


4.348 


.69729 




53 


4.234 


.70373 




58 


4.096 


.71155 




63 


3.908 


.72219 




68 


3.616 


.73872 




73 


3.193 


.76266 


74 


14 


4.528 


.68710 




19 


4.453 


.69134 




24 


4.419 


.6932t; 




29 


4.390 


.69491 




34 


4.353 


.69700 




39 


4.301 


. 69994 




44 


4.235 


.70368 




49 


4.146 


.70872 




54 


4.040 


.71472 




59 


3.906 


.72230 




64 


3.719 


.73289 




69 


3.423 


.74964 




74 


3.005 


.77330 


75 


10 


4.350 


. 69717 




15 


4. .310 


. 69943 




20 


4.242 


.70329 




25 


4.216 


. 70475 




30 


4.188 


. 70634 




35 


4.152 


.70838 




40 


4.101 


.71126 




45 


4.040 


.71472 



134 



NOETHAMPTON EXPERIENCE TABLES. 



Table VIII — (Continued). 

Ages. Single 

Older. Younger. Annuity. Premium. 

75 50 3.951 .71975 

55 3.852 .72536 

60 3.721 .73277 

05 3.533 .74341 

70 3.236 .76023 

75 2.827 .78337 

76 11 4.148 .70861 

16 4.101 .71126 

21 4.046 .71438 

26 4.024 .71562 

3l'. 3.997 .71715 

36 3.962 .71914 

41 3.912 .72197 

46 3.853 .72530 

51 3.768 .73012 

56 3.674 .73543 

01 ■ 3.546 .74268 

06 3.357 .75337 

71 3.059 .77024 

70 2.668 .79238 

77 12 3.943 .72021 

17 3.892 .72310 

22 3.850 .72547 

27 3.829 .72666 

32 3.804 .72807 

37 3.770 .73000 

42 3.722 .73272 

47 3.666 .73589 

52 3.586 .74041 

57 3.494 .74562 

62 3.371 .75258 

67 3.180 .76340 

72 2.882 .78027 

77 2.511 .80126 

78 13 3.729 .73232 

18 -3.677 .73526 



TWO LIVES ANNUITIES SINGLE PREMIUMS. 135 



Table VIII — 


■ (Continued). 




Ages. 




Single 


Older. Younger. 


Annuity. • 


Premium. 


78 23 


3.646 


.73702 


28 


3.626 


.73815 


33 


3.602 


.73951 


38 


3.570 


.74132 


43 


3.525 


.74387 


48 


3.469 


.74704 


53 


3.396 


.75117 


58 


3.308 


.75615 


63 


3.188 


.76295 


68 


2.996 


.77381 


73 


2.701 


.79051 


78 


2.346 


.81060 


79 14 


3.497 


. 74545 


19 


3.447 


.74828 


24 


3.424 


.74958 


29 


3.406 


.75060 


34 


3.384 


.75185 


39 


3.352 


.75366 


44 


3.312 


.75593 


49 


3.256 


.75909 


54 


3.189 


.76289 


59 


3.105 


.76764 


64 


2.990 


. 77415 


69 


2.799 


.78496 


74 


2.511 


.80126 


79 


2.161 


.82107 


80 10 


3.281 


.75768 


15 


3.259 


.75892 


20 


3.214 


.76147 


25 


3.198 


.76238 


30 


3.181 


.76334 


35 


3.160 


.76453 


40 


3.130 


.76623 


45 


3.093 


.76832 


50 


3 . 0'39 


.77138 


55 


2.978 


.77483 



136 



NOKTHAMPTON EXPEKIENCE TABLES. 



Table VIII- 


- (Continued). 




Ages. 
Older. Younger. 




Single 


Annuity. 


Premium. 


80 60 


2.899 


: 77930 


65 


2.786 


.78570 


70 


2.598 


.79634 


75 


2.323 


.81191 


80 


1.969 


.83194 


81 11 


3.054 


.77052 


16 


3.028 


. 77200 


21 


2.992 


.77404 


26 


2.979 


.77477 


31 


2.963 


.77568 


36 


2.944 


.77675 


41 


2.914 


.77845 


46 


2.881 


.78032 


51 


2.829 


.78326 


56 


2.774 


.78637 


61 


2.699 


.79062 


66 


2.587 


.79696 


71 


2.402 


. 80744 


76 


2.147 


.82186 


81 


1.786 


.84230 


82 12 


2.833 


.78304 


17 


2.804 


.78468 


22 


2.777 


.78620 


27 


2.765 


.78689 


32 


2.751 


.78768 


37 


2.733 


.78870 


42 


2.705 


.79029 


47 


2.673 


.79209 


52 


2.627 


.79469 


57 


2.574 


.79769 


62 


2.504 


.80166 


67 


2.393 


. 80794 


72 


2.211 


.81824 


77 


1.975 


.83161 


82 


1.606 


.85249 


83 13 


2.628 


.79464 



TWO LIVES ANNUITIES SINGLE PREMIUMS. 137 



Table VIII — (Continued). 

Agbs. Single 

Older. Younger. Annuity. Premium. 

83 18 2.598 .79634: 

23 2.579 .79741 

28 2.568 .79804 

33 2.555 .79878 

38 2.537 .79979 

43 2.511 .80126 

48 2.481 .80296 

53 2.438 .80540 

58 2.388 .80823 

63 2.321 .81202 

68 2.211 .81824 

73 2.032 .82838 

78 , 1.810 .84094 

83 1.441 .86183 

84 14 2.472 .80347 

19 2.442 .80517 

24 2.429 .80591 

29 2.418 .80653 

34 2.406 .80721 

39 2.388 .80823 

44 2.365 .80953 

49 2.334 .81128 

54 2.295 .81349 

59... 2.247 .81620 

64... 2.182 .81989 

69 2.071 .82617 

74 1.894 .83619 

79 1.672 .84876 

84 1.330 .86811 

85 15 2.327 .81168 

20 2.299 .81326 

25 2.290 .81377 

30 2.280 .81434 

35 2.268 .81502 

40 2.251 .81598 

45 2.230 .81717 



138 



NOBTHAMPTON EXPERIENCE TABLES. 



Table VIII — (Continued). 

Ages. Single 

Older. Younger. Annuity. Premium. 

85 50 2.198 .81898 

55 2.164 .820,90 

60 2.118 .82351 

65 2.053 .82719 

70 1.941 .88352 

75 1.769 .84326 

80 1.539 .85628 

85 1.232 .87366 

86 16 2.194 .81920 

21 2.171 .82051 

26 2.163 .82096 

31 2.154 .82147 

36 2.143 .82209 

41 2.126 .82306 

46 ."... 2.107 .82413 

51 2.077 .82583 

56 2.044 .82769 

61 2.000 .83019 

66 1.936 .83381 

71 1.823 .84021 

76 1.661 .84937 

81 1.417 .86318 

86 1.149 .87836 

87 17 2.069 .82628 

22 2.051 .82730 

27 2.044 .82769 

32 2.036 .82815 

37 2.026 .82872 

42 2.009 .82968 

47 1.991 .83069 

52 1.963 .83228 

57 1.932 .83404 

62 ■ 1.891 .83636 

67 1.826 .84004 

72 1.713 .84643 

77 1.562 .85498 



TWO LIVES — ANNUITIES — SINGLE PEEMITJMS. 139 



Table VIII — (Continued). 

Ages. Single 

Older. Younger. Annuity. Premium. 

87 82 1.303 .86964 

87 1.0'78 .88238 

88 18 1.965 .S3217 

23 .■ 1.953 .83285 

28 1.946 .83324 

33 1.939 .83364 

38 1.929 .83421 

43 1.914 .83505 

48 1.895 .83614 

53 1.870 .83755 

58 1.841 .83919 

63 '. 1.802 .84140 

68 1.737 .84507 

73., 1.625 .85142 

78 1.483 .85945 

83 1.212 .87480 

88 1.044 .88430 

89 19 1.822 .84037 

24 1.814 .84071 

29 1.808 .84106 

34 1.802 .84140 

39 1.792 .84197 

"44 1.779 .84270 

49 1.761 .84371 

54 1.740 .84491 

59 1.713 .84643 

64 1.678 .84842 

69 1.616 .85192 

74 1.508 .85804 

79 1.373 .86568 

84. 1.124 .87977 

89 .984 .88769 

90 20 1.638 .85068 

25 1.633 .85096 

30 1.628 .85125 

35 1.622 .85159 



140 



NOETHAMPTON EXPEEIENCB TABLES. 



Table VIII — (Continued). 

Ages. Single 

Older. Younger. Annuity. Premium. 

90 40 1.614 .85203 

45 1.604 .85260 

50 1.590 .85340 

55 1.570 .85453 

60 1.547 .85583 

65 1.515 .85764 

70 1.459 .86081 

75 1.361 .86636 

80 .' 1.234 .87354 

85 1.021 .88560 

90 .895 .89274 

91 31 1.382 .86517 

26 1.379 .86534 

31 1.376 .86551 

36 1.371 .86579 

41 1.364 .86619 

46 1.356 .86664 

51 1.343 .86738 

56 1.330 .86811 

61 1.311 .86919 

66 1.285 .87066 

71 1.238 .87332 

76 1.160 '.87774 

81 1.044 .88430 

86 .879 .89364 

91 .737 .90168 

92 22 1.107 .88073 

27 1.105 .88085 

32 1.102 .88102 

37 1.099 .88119 

42 1.094 .88147 

47 1.089 .88175 

52 1.079 .88232 

57 1.069' .88289 

62 1.055 .88368 

67 1.035 .88481 



TWO LIVES ANNUITIES SINGLE PREMIUMS. 141 



Table VIII — ' ( Continued ) . 

Ages. Single 

Older. Younger. Annuity. Premium. 

92 72 .997 ,88696 

77 .942 .89008 

82 .840 .89585 

87 .725 .90236 

92 .569 .91119 

93 23 .788 .89880 

28 .786 .89891 

33 .785 .89897 

38 .783 .89908 

43... .779 .89930 

48 .776 .89947 

53 .770 .89981 

58 .763 .90021 

63 .754 .90071 

68 .740 .90151 

7.3 .714 .90298 

78 .679 .90496 

83 .599 .90949 

88 .541 .91277 

93 357 .92318 

94 24 .508 .91464 

29 .507 .91469 

34 .506 .91475 

39 .505 .91481 

44 .503 .91492 

49 .501 .91503 

54 .498 .91521 

59 .494 .91543 

64 .489 .91572 

69 .480 .91623 

74 .464 .91713 

79 .443 .91832 

84 .394 .92109 

89 .365 .92274 

94 .197 .93224 

95 25 .232 .9302T 



142 



NORTHAMPTON EXPERIENCE TABLES. 



Table VIII — {Concluded). 

Ages. Single 

Older. Younger. Annuity. Premium. 

95 30 .231 .93032 

35 .231 .93032 

40 .231 .93032 

45 .230 .93038 

50 .229 .93043 

55 .228 .93049 

60 .226 .93060 

65 .224 .93071 

70 .220 .93094 

75 .213 .93134 

80 .204 .93185 

85 .183 .93304 

90 : .174 .93354 

95 .058 .94012 



CARLISLE MORTALITY TABLE. 



143 



0. 

1. 

3 . 

3. 

4. 

5.. 

6. 

i . 
■8. 

9. 
10. 
11. 
12. 
13. 
14. 
15. 
16. 
17. 
18. 
19. 
20. 
21. 
22. 
23. 
24. 
25. 
26. 
27. 
28. 
29. 
30. 



Table IX. 






Table of Mortality. 




Ix 


dx 


Expec- 
tation. 


10,000 


1,539 


38.72 


8,461 


682 


' 44.68 


7,779 


505 


47.55 


7,274 


276 


49.82 


6,998 


201 


50.76 


6,797 


121 


51.25 


6,676 


82 


51.17 


6,594 


58 


50.80 


6,536 


43 


50.24 


6,493 


33 


'49.57 


6,460 


29 


48.82 


6,431 


31 


48.04 


6,400 


32 


47.27 


6,368 


33 


46.51 


6,335 


35 


45.75 


6,300 


39 


45.00 


6,261 


42 


44.27 


6,219 


43 


43.57 


6,176 


43 


42.87 


6,133 


43 


42.17 


6,090 


43 


41.46 


6,047 


42 


40.75 


6,005 


42 


40.04 


5,963 


42 


39.31 


5,921 


42 


38.59 


5,879 


43 


37.86 


5,836 


43 


37.14 


5,793 


45 


36.41 


5,748 


50 


35.69 


5,698 


56 


35.00 


5,642 


57 


34.34 


5,585 


57 


33.68 


5,528 


56 


33.03 



144 



CAKLISLE EXPEKIENCE TABLES. 



Table IX — (Continued). 



, Expeo- 

Age. Ix "X tation. 

33 5,472 55 32.36 

34 5,417 55 31.68 

35 5,362 55 31.00 

36 5,307 56 30.32 

•37 5,251 57 29.64 

38 5,194 58 28.96 

39 5,136 61 28.28 

40 5,075 66 27.61 

41 5,009 69 26.97 

42 4,940 71 26.34 

43 4,869 71 25.71 

44 4,798 71 25.09 

45 4,727 70 24.46 

46 4,657 69 23.82 

47 4,588 67 23.17 

48 4,521 63 22.50 

49 4,458 61 21.81 

50 4,397 59 21.11 

51 4,338 62 20.39 

52 4,276 65 19.68 

53 4,211 68 18.97 

54 4,143 70 18.28 

55 4,073 73 17.58 

56 4,000 76 16.89 

57 3,924 82 16.21 1 

58 3,842 93 15.55 

59 3,749 106 14.92 

60 3,643 122 14.34 

61 3,521 126 13.82 

62 3,395 127 13.31 

63 3,268 125 12.81 

64 3,143 125 12.30 

65 3,018 124 11.79 

66 2,894 123, 11.27 

67 2,771 123 10.75 

68 2,648 123 10.23 



CAELISLE MOKTALITY TABLE. 145 



Table IX — (Concluded). 










Expec- 


Age. 


Ix 


dx 


tation. 


69 


2,525 


124 


9.70 


70 


2,401 


124 


9.18 


71 


2,277 


134 


8.65 


72 


2,143 


146 


8.16 


73 


1,997 


156 


7.72 


74 


1,841 


166 


7.33 


75 


1,675 


160 


7.01 


76 


1,515 


156 


6.69 


77 


' 1,359 


146 


6.40 


78 


1,213 


132 


6.12 


79 


1,081 


128 


5.80 


80 


953 


116 


5.51 


81 


837 


112 


5.21 


82 


725 


102 


4.93 


83 


623 


94 


4.65 


84 


529 


84 


4.39 


85 


445 


78 


4.12 


86 


367 


71 


3.90 


87 


296 


64 


3.71 


88 


232 


51 


3.59 


89 


181 


39 


3.47 


90 


142 


37 


3.28 


91 


105 


30 


3.26 


92 


75 


21 


3.37 


93 


54 


14 


3.48 


94 


• 40 


10 


3.53 


95 


30 


7 


3.53 


96 


23 


5 


3.46 


97 


18 


4 


3.28 


98 


14 


3 


3.07 


99 


11 


2 


2.77 


100 


9 


2 
2 


2.28 


101 


7 


1.79 


102 


5 


2 


1.30 


103 


3 


2 


.83 


104 


1 


1 


.50 


10 






' 



146 



CARLISLE EXPERIENCE TABLES. 



Table X — ! 


Single Life — Commutation 






Columns. 




!ARI 


JSLE Table 


of Mortality, icitli 7i 
Per Annum. 


nterest at ^i 


Age. 


D.. 


N,. 


M,, 





10000.0000 


130830.3190 


3769.989540 


1 


8058.1952 


120830.3190 


2304.275259 


2 


7055.7823 


112772.1238 


1685.681154 


3 


6283.5547 


105716.3415 


1249.443166 


4 


•5757.2719 


99432.7868 


1022.377285 


5 


5325.6273 


93675.5149 


864.888527 


6 


4981.7340 


88349.8876 


774.596464 


7 


4686.2327 


83368.1536 


716.320595 


8 


4423.8221 


78681.9209 


677.063912 


9 


4185.4457 


74258.0989 


649.345728 


10 


,3965.8796 


70072.6532 


629.086591 


11 


3760.0725 


66106.7736 


612.130892 


12 


3563.7595 


62346.7011 


594.868932 


13 


3377.0864 


58782.9416 


577.898649 


14 


3199.6055 


55405.8552 


561.231407 


15 


3030.4077 


52206.2497 


544.395808 


16 


2868.2362 


49175.8420 


526.529459 


17 


2713.3291 


46307.6058 


508.204998 


18 


2566.2555 


43594.2767 


490.337610 


19 


2427.0364 


41028.0212 


473.321050 


20 


2295.2569 


38600.9848 


457.114802 


21 


2170.5244 


36305.7278 


441.680280 


22 


2052.8085 


34135.2034 


427.322585 


23 


1941.3817 


32082.3949 


413.648590 


24 


1835.9121 


30141.0132 


400.625738 


25 


1736.0850 


28305.1011 


388.223022 


26 


1641.3209 


26569.0161 


376.129671 


27 


1551.6453 


24927.6952 


364.612193 


28 


1466.2782 


23376.0499 


353.132979 


29 


1384.3081 


21909.7717 


340.985663 


30 


1305.4316 


20525.4636 


328.028526 


31 


1230.7076 


19220.0320 


315.468036 





SINGLE LIFE - 


- COMMUTATION COLUMNS. 147 




Table X — (Continued). 




Age. 


D.. 


N. 


M,. 


32 


1160.1402 


17989.^244 


303.505664 


33 


1093.7025 


16829.1842 


292.312802 


34 


1031.1520 


15735.4816 


281.84.3288, 


35 


972.0785 


14704.3297 


271.872322 


36 


916.2929 


13732.2512 


262.376164 


37 


863.4515 


12815.9583 


253.167770 


38 


813.4082 


11952.5068 


244.241264 


39 


766.0240 


11139.0^985 


235.590682 


40 


720.8818 


10373.0746 


226.925895 


41 


677.6255 


9652.1928 


217.997309 


42 


636.4677 


8974.5672 


209.107375 


43 


597.4477 


8338.0995 


200.395363 


44 


560.7007 


7740.6518 


192,098209 


45 


526.0986 


7179.9511 


184.196157 


46 


493.6265 


6653.8525 


176.776389 


47 


463.1550 


6160.2260 


169.810893 


48 


434,6585 


5697.0710 


163.369372 


49 


408.1919 


5262.4125 


157.600846 


50 


383.4348 


4854.2206 


152.281418 


51 


360.2760 


4470.7858 


147.381399 


52 


338.2160 


4110.5099 


142.477425 


53 


317.2140 


3772.2939 


137.580984 


54 


297.2301 


3455.0798 


132.702479 


55 


278.2934 


3157.8498 


127.919631 


56 


260.2910 


2879.5563 


123.169319 


57 


243.1862 


2619.2653 


118.459290 


58 


226.7660 


2376.0791 


113.619411 


59 


210.7399 


2149.3131 


108.391667 


60 


195.0299 


1938.5731 


102.716902 


61 


179.5225 


1743.5432 


96.496585 


62 


164.8554 


1564.0208 


90.378240 


63 


151.1319 


1399.1654 


84.504998 


64 


138.4297 


1248.0334 


78.999522 


65 


126.5945 


1109.6037 


73.756212 


66 


115.6125 


983.0093 


68.802532 


67 


105.4274 


867.3968 


64.122788 



148 



OABLISLE EXPERIENCE TABLES. 





Table X- 


- (Concluded). 




Age. 


D.. 


N.. 


M,. 


68 


95.95014 


761.9694 


59.665889 


69 


87.13644 


666.0192 


55.421223 


70 


78.91168 


578.8828 


51.345819 


71 


71.27263 


499.9711 


47.464482 


72 


63.88407 


428.6985 


43.469865 


73 


56.69689 


364.8144 


39.324775 


74 


49.77894 


308.1175 


35.106679 


75 


43.13377 


258.3386 


30.831930 


76 


37.15574 


215.2048 


26.907892 


77 


31.74266 


178.0491 


23.264142 


78 


26.98333 


146.3064 


20.016354 


79 


22.90187 


119.32308 


17.219825 


80 


19.22866 


96.42121 


14.637172 


81 


16.08393 


77.19255 


12.408096 


82 


13.26831 


61.10861 


10.358372 


83 


10.85866 


47.84031 


8.580550 


84 


8.781214 


36.98165 


7.020183 


85 


7.035090 


28.20043 


5.692211 


86 


5.525687 


21.16534 


4.517814 


87 


4.244462 


15.63966 


3.499717 


88 


3.168324 


11.39519 


2.625696 


89 


2.354133 


8.226869 


1.962377 


90 


1.758941 


5.872736 


1.479288 


91 


1.238691 


4.113795 


1.042796 


92 


.8426475 


2.875104 


.705737 


93 


.5778151 


2.032457 


.481032 


94 


.4076296 


1.454642 


.338361 


95 


.2911641 


1.047012 


.241306 


96 


.2125961 


.7558478 


.176603 


97 


.1584567 


.5432517 


.132588 


98 


.1173753 


.3847950 


.099052 


99 


.0878318 


.2674197 


.075098 


100 


.0684404 


.1795879 


.059889 


101 


.0506966 


.1111474 


.045404 


102 


.0344875 


.0604509 


.031609 


103 


.0197071 


.0259634 


.018471 


104 


.0062562 


.0062562 


.005958 



SINGLE LIFE ANNUITIES SINGLE PEEMITJMS. 149 

Table XI — Single Life. 

ANNUITIES AND SINGLE PBEMIUMS PEE $1. 

CARLISLE Table of Mortality, with Interest at 5^ 
Per Annum. 

Age. 



1 

2 

3 

4 

5.- 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

31 



Annuity. 


Single 
Premium. 


12.083 


.37700 


13.995 


.28595 


14.983 


.23891 


15.824 


.19886 


16.271 


.17757 


16.590 


.16238 


16.735 


.15548 


16.790 


.15286 


16.786 


.15305 


16.742 


.15514 


1^.669 


.15862 


16.581 


.16281 


16.494 


.16695 


16.406 


.17114 


16.316 


.17543 


16.227 


.17967 


16.144 


.18362 


16.066 


.18733 


15.987 


.19110 


15.904 


.19505 


15.817 


.19919 


15.726 


.20352 


15.628 


.20819 


15.525 


.21310 


15.417 


.21824 


15.303 


.22367 


15.187 


.22919 


15.065 


.23500 


14.942 


.24086 


14.827 


.24633 


14.723 


.2512!) 


14.617 


.25633 



150 



CAELISLE EXPERIENCE TABLES. 



Table XI — (Continued). 

Single 

Age. Annuity. Premium. 

;]-! 14.506 .26162 

33 14.387 .26729 

34 14.260 .27333 

35 14.127 .27967 

36 13.9ST .28633 

37 13.843 .29319 

38 13.695 .30024 

39 13.542 .30752 

40 13.390 .31477 

41 13.245 .32167 

42 13.101 .32852 

43 12.957 .33538 

44 12.806 .34257 

45 12.648 .35010 

46 12.480 .35810^ 

47 12.301 .36662 

48 12.107 .37586 

49 11.892 .38610 

50 11.660 .39714 

51 11.410 .40905 

52 11.154 .42121 

53 10.892 .43371 

54 10.624 .44648 

55 10.347 .45967 

56 10.063 .47319 

57 9:771 .48710 

58 9.478 .50105 

59 9.199 .51433 

60 8.940 .52667 

61 8.712 .53752 

62 8.487 .54824 

63 8.258 .55914 

64 8.016 .57067 

65 7.765 .58262 

66 7.503 .59510 

67 7.227 .60824 



SINGLE 


LIFE ANNUITIES SINGLE PREMIUMS. lOl 




Table XI — (Concluded). 




Age. 


Annuity. 


Single 
Premium. 


68... 


6.941 


.62186 


69. . . 


6 . 643 


.63605 


70... 


6.336 


.65067 


71... 


6.015 


.66595 


72... 


5.711 


. 6804:i 


73... 


5.435 


.69357 


74... 


5.190 


.70524 


75... 


4.989 


.71481 


76... 


4.792 


.72419 


77... 


4.6O19 


.73291 


78... 


4.422 


.74181 


79... 


4.210 


.75191 


80... 


4.015 


.76119 


81... 


3.799 


.77148 


82... 


3.606 


.78067 


83... 


3.406 


.79019 


84... 


3.211 


.79948 


85... 


3.009 


.80910 


86... 


2.830 


.81762 


87... 


2.685 


. 82452 


88... 


2.597 


.82870 


89. . . 


2.495 


.83357 


90... 


2.339 


. 84103 


91... 


2.321 


.84186 


92... 


2.412 


.83752 


93... 


2.518 


.83248 


94... 


•. 2.569 


.83005 


95... 


2.596 


.82876 


96... 


2.555 


.83071 


97 


2.428 


83676 


98... 


2.278 


.84391 


99... 


2.045 


.85500 


100... 


1.624 


. 87505 


101... 


1.192 


.89562 


102... 


0.753 


.91653 


103... 


0.317 


.93728 



152 



CAELISLE EXPEKIENCE TABLES. 



Table XII — Two Lives 


— Commutation 




Columns. 




CARLIS 


LE Table of Mortality, 


with Interest at 




Per Annum (Makehamised) . 


Equal 
Ages. 


D.X. 


N,,. 


10... 


. 2561930000 


40416200000 


11... 


. 2415560000 


37854270000 


12... 


2277030000 


35438710000 


13... 


2145950000 


33161680000 


14... 


2021760000 


31015730000 


15... 


1904240000 


28993970000 


16... 


1792880000 


27089730000 


17... 


1687420000 


25296850000 


18... 


1587500000 


23609430000 


19... 


1492730000 


22021930000 


20... 


1402990000 


20529200000 


21... 


1318030000 


19126210000 


22... 


1237410000 


17808180000 


23... 


1160980000 


16570770000 


24... 


1088470000 


15409790000 


25... 


1018380000 


14321320000 


26... 


952616000 


13302943000 


27... 


890982000 


12350327000 


28... 


833182000 


11459345000 


29... 


778950000 


10626163000 


30... 


728117000 


9847213000 


31. .. 


680412000 


9119096000 


32... 


635687000 


8438684000 


33... 


593709000 


7802997000 


34. . . 


554350000 


7209288000 


35... 


517410000 


6654938000 


36... 


482753000 


6137528000 


37... 


450232000 


5654775000 


38... 


419708000 


5204543000 


39... 


391072000 


4784835000 


40... 


364190000 


4393763000 



TWO LIVES — COMMUTATION COLUMNS. 



153 





Table XII- 


- (Continued). 


jqual 


' D,,. 


N.,. 


41... 


338953000 


4029573000 


42... 


315246000 


3690620000 


43... 


293009000 


3375374000 


44... 


272051000 


, 3082365000 


45... 


252501000 


2810314000 


46... 


234084000 


255781300a 


47... 


.* 216792000 


2323729000 


48... 


200555000 


2106937000 


49... 


185304000 


1906382000 


50... 


170984000 


1721078000 


51... 


157538000 


1550094000 


52... 


144923000 


1392556000 


53... 


133084000 


1247633000 


54... 


121977000 


1114549000 


55... 


111565000 


992572000 


56... 


101803000 


881007000 


57... 


92668000 


779204300 


58... 


84116400 


686536300 


59. . . 


76129200 


602419900 


60... 


68669200 


526290700 


61... 


61721000 


457621500 


62... 


55256600 


395900500 


63... 


49255400 


340643900 


64... 


43700400 


291388500 


65... 


38572400 


247688100 


66... 


33852200 


209115700 


67... 


29526900 


175263500 


68... 


25580400 


145736600 


69... 


21997800 


120156200 


70... 


18764200 


98158400 


71... 


15864300 


79394200 


72... 


13282200 ^ 


63529900 


73... 


11002700 


50247700 


74... 


9009320 


39245010 


75... 


7283550 


30235690 


76... 


5806490 


22952140 



154 



CABLISLE EXPERIENCE TABLES. 





Table XII — {Concluded). 


Equal 
Ages. 


D... 


N.x: 


77. . . 


4558940 


17145650 


78... 


3520100 


12586710 


79... 


2668730 


9066610 


80... 


1983150 


6397880 


81... 


1441740 


4414730 


82... 


1023280 


2972990 


83... 


707470 


1949711 


84... 


475290 


1242241 


S5... 


309407 


766951 


86... 


194608 


457544 


87... 


117883 


262936 


88... 


68520.7 


145053.4 


89... 


38070.8 


76532.7 


90. . . 


20133.7 


38461.9 


91. . . 


10087.3 


18328.2 


92... 


4763.49 


8240.93 


93. . . 


2108.51 


3477.44 


94... 


869.452 


1368.932 


95... 


331.770 


499.480 


96... 


116.292 


167.710 


97... 


37.1483 


51.4188 


98... 


10.7189 


' 14.2705 


99... 


2.76719 


3.55160 


100... 


.63245 


.78441 


101. . . 


.12644 


• .15196 


102... 


.02186 


.02552 


103... 


.00322 


.00366 


101. . . 


.00040 


. 00044 


105... 


.00004 


.00004 



TWO LIVES ANNUITIES SINGLE PEEMItJMS. 155 



. Table XIII — Two Lives. 

ANNUITIES AND SINGLE PREMIUMS PEE $1. 

CAELISLE Table of Mortality, with Interest at 5;^ 
Per Annum (Makehamised) . 

Equal Single 

Ages. Annuity. Premium. 

10 14 . 7757 . 24876 

11 14.6710 .25376 

12 14.5636 .25886 

13 14.4531 .26415 

14 14.3410 .26947 

15 14.2260 .27495 

16 14.1096 .28048 

17 13.9914 .28614 

18 13.8721 .29180 

19 13.7528 .29748 

20 13.6325 .30319 

21 13.5112 .30900 

22 13.3915 .31466 

"23 13.2731 -.32034 

24 13.1573 .32586 

25 ;. 13.0628 .33034 

26 .. .: .. 12.9646 .33500 

27 12.8615 .33990 

28 ,. 12.7537 .34505 

29 12.6416 .35038 

30... 12.5242 .35600 

31 12 . 4023 . 36180 

32 12.2749 .36786 

33 12.1428 .37415 

34 12.0049 .38071 

35 11.8620 .38752 

36 11.7136 .39457 

37 11.5597 .40190 

38 11.4004 .40952 

39 11.2352 .41738 

40 11.0645 .42547 



156 



CAELISLE EXPERIENCE TABLES. 



Table XIII — (Continued). 




Equal 

Ag s. 


Annuity. 


Single 
Premium. 


41 


10.8883 


.43391 


42 


10.7071 


.44253 


43 


10.5197 


.45143 


44 


10.3301 


.46048 


45 


10.1299 


.47000 


46 


9.9269 


.47967 


47 


9.7187 


.48957 


48 


9.5055 


.49971 


49 


9.2879 


.51010 


50 


9.0657 


.52066 


51 


8.8395 


.53143 


52 


8.6089 


. 54243 


53 


8.3748 


.55357 


54 


8.1374 


.56491 


55 


7.8968 


.57634 


56 


7.6540 


.58791 


57 


7.4086 


.59957 


58 


7.1617 


.61133 


59 


6.9131 


.62319 


60 


6.6641 


.63505 


61 


6.4144 


.64695 


62 


6.1648 


.65881 


63 


5.9159 


.67066 


64 


5.6679 


.68248 


65 


5.4214 


.69424 


66 


5.1773 


.70586 


67 


4.9357 


.71733 


68 


4.6972 


.72872 


69 


4.4622 


.73990 


70 


4.2312 


.75090 


71 


4.0046 


.76166 


72 


3.7831 


.77224 


73 


3.5669 


.78253 


74 


3.3560 


.79257 


75 


3.1512 


.80233 


76 


2.9528 


.8117ft 



TWO LIVES ANNUITIES SINGLE PREMIUMS. 157 



Table XIII — (Concluded). 

Equal Single 

Ages. Annuity. Premium. 

77 2.7609 .82090 

78 2.5757 .82971 

79 2.3974 .83824 

80 2.2261 .84638 

81 2.0621 .85419 

82 1.9054 .86366 

83 1.7559 .86876 

84 * 1.6136 .87552 

85 1.4788 .8819^ 

86 1.3511 .88805 

87 1.2305 .89376 

88 1.1169 .89919 

89 1.0103 .90429 

90 .9103 .90905 

91 .8170 .91348 

92 .7300 .91762 

93 .6492 .92147 

94 .5745 .92500 

95 .5055 .92828 

96 .4422 .93133 

97 .3841 .93410 

98 . .3313 .93662 

99 .2834 .93891 

100 .2402 .94095 



158 



CAELISLE EXPERIENCE TABLES. 



Table XIV — Theee Lives ■ 
Columns. 



Commutation 



Equa' 
Ages. 



CARLISLE Table, of Mo 
Per Annum 

10 165500000000000 

11 155263000000000 

12 145609000000000 < 

13 136509000000000 

14 127915000000000 

15 119812000000000 

16 112161000000000 

17 104940000000000 

18 98123500000000 

19 91679600000000 

20 85600000000000 

21 79868400000000 

22 74448300000000 

23 69329200000000 

24 64490700000000 

25 59803700000000 

26 55441900000000 

27 51387700000000 

28 47616800000000 

29 44107200000000 

30 40845200000000 

31 37808700000000 

32 34985900000000 

33 32358100000000 

34 2991530000,0000 

35 27641700000000 

36 25526700000000 

37 23558900000000 

38 21727900000000 

39 20025100000000 

40 18440700000000 



rtality, with Interest at 5^ 
(Makehamized) . 

^X.lW. 

2377904000000000 

2212404000000000 

2057141000000000 

1911532000000000 

1775023000000000 

1647108000000000 

1527296000000000 

1415135000000000 

1310195500000000 

1212072000000000 

1120392400000000 

1034792400000000 

954924000000000 

880475700000000 

811146500000000 

746655800000000 

686852100000000 

631410200000000 

580022500000000 

532405700000000 

488298500000000 

447453300000000 

409644600000000 

374658700000000 

342300600000000 

312385300000000 

284743600000000 

259216900000000 

235658000000000 

213930100000000 

193905000000000 



THREE LIVES COMMUTATION COLUMNS. 159 





Table XIV- 


- {Continued). 


}ual 


'^XXX. 


N.... 


41 


16966400000000 


175464300000000 


42 


15593700000000 


158497900000000 


43 


14318300000000 


142904200000000 


44 


13127800000000 


128585900000000 


45 


12026900000000 


115458100000000 


46 


11000500000000 


103431200000000 


47 


10046500000000 


92430700000000 


48 


9159980000000 


82384250000000 


49 


8336120000000 


73224270000000 


50 


7571200000000 


64888150000000 


51 


6861300000000 


57316950000000 


52 


6203340000000 


50455650000000 


53 


5593800000000 


44252310000000 


54 


5029540000000 


38658510000000 


55 


4508160000000 


33628970000000 


56 


4026610000000 


29120810000000 


57 


3583360000000 


25094200000000 


58 


3175490000000 


21510840000000 


59 


2801630000000 


18335350000000 


60 


2459360000000 


15533720000000 


61 


2147450000000 


13074360000000 


62 


1863990000000 ' 


10926910000000 


63 


1607470000000 


9062920000000 


64 


1376530000000 


7455450000000 


65 


1169680000000 


6078920000000 


66 


985430000000 


4909243000000 


67 


822558000000 


3923813000000 


68 


679670000000 


3101255000000 


69 


555390000000 


2421585000000 


70 


448352000000 


1866195000000 


71 


357149000000 


1417843000000 


72 


280363000000 


1060694000000 


73 


216601000000, 


780331000000 


74 


164453000000' 


563730000000 


75 


122493000000 


399277000000 


76 


89343500000 


276784500000 



160 



CARLISLE EXPERIENCE TABLES. 



Equal 



Table XIV— (Concluded). 



Ages. 


^xxx. 


'■^xxx. 


77 


63691900000 


187441000000 


78 


44280800000 


123749100000 


79 


29952600000 


79468300000 


80 


19661000000 


49515700000 


81 


12488100000 


29854700000 


82 


7651680000 


17366670000 , 


83 


4507320000 


9714990000 


84 


2543250000 


5207670000 


85 


1368800000 


2664420000 


86 


699648000 


1295626000 


87 


387995000 


595978000 


88 


153484000 


257983000 


89 


65134700 


104499800 


90 


25668600 


39365100 


91 


9327680 


13696510 


92 


3101660 


4368830 


93 


935976 


1267175 


94 


253961 


331199 


95 


61340.4 


77238.5 


96 


13043.9 


15898.1 


97 


2413.17 


2854.28 


98 


383.265 


441.116 


99 


51.5144 


57.8518 


100 


5.7678 


6.3374 


101 


.5283 


.5696 


102 


.0389 


.0413 


103 


.0023 


.0024 


104 


.0001 


.0001 



THEEB LIVES ANNUITIES SINGLE PEEMIUMS. 161 



Table XV — Thbee Lives. 

ANNUITIES AND SINGLE PEEMIUMS PEE $1. 

CARLISLE Table of Mortality, with Interest at 5,'!! 
Per Annum (Makehamized) . 

Equal . Single 

Ages. Annuity. Premium. 

10 13.3680 .31581 

11 13.2494 .32147 

12 13.1278 .32724 

13 13.0030 .33319 

14 12.8766 .33919 

15 12.7474 .34538 

16 .' 12.6170 .35157 

17 12.4852 .35786 

18 12.3525 .36415 

19 12.2207 .37043 

20 12.0887 .37671 

21 11.9562 .38304 

22 11.8267 .38919 

23 '. 11.6999 .39524 

24 11.5777 .40105 

25 11.4851 .40547 

26 11.3887 .41005 

27 11.2872 .41491 

28 .- 11.1810 .41995 

29 11.0707 .42519 

30 10.9549 .43071 

31 10.8347 .43643 

32 10 . 7088 . 44243 

33 10.5785 .44862 

34 10.4423 .45514 

35 10.3012 .46185 

36 10.1547 .46881 

37 - 10.0029 .47605 

38 9.8459 .48352 

39 9.6831 .49129 

40 9.5151 .49928 

11 



162 



CAELISLE EXPEBIENCB TABLES. 



Equal 



Table XV — (Continued). 

Annuity. 

9.3419 


single 
Premium. 

.50752 


9.1642 


.51600 


8.9805 


.52471 


«.7949 


.53357 


8.6000 


.54286 


8.4024 


.55228 


8 . 2003 


.56190 


7.9939 


.57171 


7.7840 


.58171 


7.5704 


.59190 


7.3537 


.60219 


7.1336 


.61267 


6.9110 


.62328 


6.6863 


. 63400 


6.4596 


. 64476 


6.2321 


.65561 


6.0030 


.66653 


5.7740 


. 67743 


5 . 5445 


.68833 


5.3162 


.69923 


5.0883 


.71010 


4.8621 


.72085 


4.6380 


.73152 


4.4161 


.74209 


4.1971 


.75253 


3.9818 


.76276 


3.7703 


.77286 


3.5629 


.78272 


3.3602 


.79238 


3.1623 


.80180 


2.9699 


,81095 


2.7833 


.81986 


2.6026 


. 82843 


2.4279 


.83676 


2.2596 


.84476 


2.0980 


.85248 



41. 
42. 
43, 
44. 
45, 
46, 
47, 
48, 
49, 
50, 
51, 
52 
53, 
54 
55, 
56 
57 
58 
59 
60 
61 
62 
63 
64 
65 
66 
67 
68 
69 
70 
71 
72 
73 
74 
75 
76 



THREE LIVES ANNUITIES SINGLE PREMIUMS. 163 



Table XV — (Concluded). 

Equal Single 

Ages. Annuity. Premium. 

77 ;■. 1.9429 .8598ft 

78 :. 1.7946 .86690 

79 1.6531 .87367 

80 1.5185 .88005 

81 1.3907 .88614 

82 1.2697 .89190 

83 1.1554 .89738 

84.: 1.0476 .90248 

85 .9465 .90729 

86 .8518 .91180 

87 .'7633 .91605 

88 .6809 .91995 

89 .6044 .92362 

90 .5336 .92695 

91 .4684 .93010 

92 .4085 :93290 

93 .3539 .93552 

94 .3041 .93791 

95 .2592 .94005 

96 .2188 .94195 

97 .1828 .94367 

98 .1509 .94519 

99 .1230 .94653 

100 .0987 .94767 



164 



CARLISLE EXPERIENCE TABLES. 



Table XVI — Single Life — Commutation 
Columns. 

CARLISLE Table of Mortality, with Interest at 6^ 
Per Annum. 



Lges. 


Dx. 


N, 


M:„. 





lOOOO.OOOO 


114397.1220 


3524.691199 


1 


7982.0755 


104397.1220 


2072.804399 


2 


6923.2823 


96415.0465 


1465.826827 


3 


6107.3906 


89491.7642 


1041.819091 


4 


5543.0714 


83384.3735 


823.201241 


5 


5079.1138 


77841.3021 


673.002349 


6 


4706.3166 


72762.1884 


587.702123 


7 


4385.3866 


6805'5.8718 


533.167440 


8 


4100.7673 


68670.4852 


496.777522 


9 


3843.1967 


59569.7180 


471.325888 


10 


3607.2303 


55726.5213 


452.898860 


11 


'3387.7706 


52119.2910 


437.622022 


12 


3180.6039 


48731.5204 


422.215972 


13 


2985.5669 


45550.9165 


407.213123 


14 


2801.9766 


42565.3496 


392.617191 


15 


2628.7699 


39763.3730 


378.012914 


16 


2464.6194 


37134.6031 


362.660709 


17 


2309.515'3 


34669.9838 


347.063403 


18 


2163.7232 


32360.4685 


331.998620 


19 


2027.0363 


30196.7452 


317.786561 


20 


1898.8908 


28169.7089 


304.378958 


21 


1778.7577 


26270.8181 


291.730276 


22 


1666.4181 


24492.0604 


280.075062 


23 


1561.0971 


22825.6423 


269.079577 


24 


1462.3600 


21264.5452 


258.706478 


25 


1369.7989 


19802.1852 


248.920535 


26 


1282.8113 


18432.3863 


239.468704 


27 


1201.2825 


17149.5750 


230.551882 


28 


1124.4820 


15948.2925 


221.748526 


29 


1051.6043 


14823.8104 


212.520689 


30 


982.3294 


13772.2061 


202.770522 


51 


917.3633 


12789.8768 


193.407996 





SINGLE LIFE - 


— COMMUTATION COLUMNS. lOD' 




Table XVI — {Continued). 




0[ual 
ges. 


D.. 


N.. 


M;,. 


32 


856.6045 


11872.5135 


184.575424 


33 


799.9310 


11015.9090 


176.388996 


34 


747.0668 


10215.9780 


168.803862 


35 


697.6242 


9468.9112 


161.648075 


36 


651.3853 


8771.2871 


154.897333 


37 


608.0301 


8119.9018 


148.412915 


38 


567.3866 


7511.8717 


142.186300 


39 


529.2932 


6944.4851 


136.209080 


40 


493.4026 


6415.1920 


130.278526 


41 


459.4207 


5921.7894 


124.225069 


42 


427.4454 


' 5462.3686 


118.254678 


43 


397.4546 


50'34.9233 


112.458975 


44 


369.4896 


4637.4687 


106.991330 


45 


343.4169 


4267.9791 


101.833175 


46 


319.1806 


3924.5622 


97.035528 


47 


296.6523 


3605.3816 


92.574105 


48 


275.7738 


3308.7293 


88.487212 


49 


256.5385 


3032.9556 


84.861835 


50 


238.7059 


2776.4170 


81.550245 


51 


222.1726 


2537.7111 


78.528534 


52 


206.6011 


2315.5385 


75.532914 


53 


191.9440 


2108.9374 


72.570113 


54 


178.1551 


1916.9934 


69.646013 


55 


165.2311 


1738.8383 


66.806294 


56 


153.0846 


1573.6072 


64.012500 


57 


141.6755 


1420.5226 


61.268531 


58 


130.8631 


1278.8472 


58.475513 


59 


. 120.4674 


■ 1147.9841 


55.487125 


60 


110.4351 


1027.5167 


52.273805 


61 


100.6951 


917.0816 


48.784796 


62 


91.59500 


816.3865 


45.385360 


63 


83.17877 


724.7906 


42.152892 


64 


75.46905 


641.6118 


39.151418 


65 


68.36567 


566.142& 


36.319838 


66 


61.84597 


497.7771 


33.669907 


67 


55.86549 


435.9312 


31.190133 



166 



CAKLISLB EXPEBIENCE TABLES. 





Table XVI 


— (Concluded). 




Equal 


D.. 


N.. 


M,. 


68 


50.36386 


380.0657 


28.850723 


69 


45.30611 


329.7018 


26.643733 


70 


40.64262 


284.3957 


24.544740 


71 


36.36188 


243.7531 


22.564558 


72 


32.28494 


207.3912 


20.545808 


73 


28 38244 


175.1063 


18.470777 


74 


24.68424 


146.723S 


16.379120 


75 


'21.18727 


122.0396 


14.279367 


76 


18.07870 


100.8523 


12.370066 


77 


15.29916 


82.77360 


10.613869 


78 


12.88259 


67.47444 


9.063285 


7& 


10.83084 


54.59185 


7.740740 


80 


9.007899 


43.76101 


6.530865 


81 


7.463638 


34.75311 


5.496478 


8-2 


6.098976 


27.28948 


4.554291 


83 


4.944259 


21.19050 


3.744798 


84 


3.960617 


16.24624 


3.041021 


85 


3.143124 


12.28562 


2.447712 


86 


2.445468 


9.14250O 


1.927967 


87 


1.860721 


6.697032 ' 


1.481645 


88 


1.375853 


4.836311 


1.102099 


89 


1.012645 


3.460458 


.816768 


90 


.749480 


2.447813 


.610925 


91 


.522824 


1.698333 


.426692 


92 


.352307 


1.175509 


.285769 


93 


.239303 


.823202 


.192707 


94 


.167228 


.583898 


.134177 


95 


.118322 


.416670 


.094736 


96 


.085579 


.298349 


.068690 


97 


.063183 


.212770 


.051139 


98 


.046361 


.149587 


.037893 


99 


.034365 


.103226 


.028521 


100 


.026525 


.068861 


.022627 


101 


.019463 


.042336 


.017066 


102 


.013115 


.022873 


.011820 


103 


.007424 


.009758 


.006871 


104 


.002334 


.002334 


.002202 



SlNGLiE LIFE ANNUITIES SINGLE PREMIUMS. 167 

Table XVII — Single Life. 

ANNUITIES AND SINGLE PREMIUMS PER $1. 

CAEIISLE Table of Mortality, with Interest at Qi 
Per Annum. 

Age. 



1 

2 

3 

4 

5 

6 

7 



9. 
10. 
11. 
12. 
13. 
14. 
15. 
16. 
17. 
18. 
19. 
20. 
21. 
22. 
23. 
24. 
25. 
26. 
27. 
28. 
29. 
30. 
31. 



Annuity. 


single 
Premium. 


10.439 


.35251 


12.078 


.25974 


12.925 


.21179 


13.652 


.17065 


14.042 


.14857 


14.325 


.13255 


14.460 


.12491 


14.518 


.12163 


14.526 


.12117 


14.500 


.12264 


14.448 


.12558 


14.384 


.12921 


14.321 


.13277 


14.257 


.13640 


14.191 


.14013 


14.126 


.14381 


14.067 


.14715 


14.012 


.15026 


13.956 


.15343 


13.897 


.15677 


13.835 


.16028 


13.769 


.16402 


13.697 


.16809 


13.621 


. 17240 


13.541 


.17692 


13.456 


.18174 


13.368 


.18672 


13.275 


.19198 


13.182 


.19725 


13.096 


.2021] 


13.020 


.20642 


12.942 


.21083 



168 



CAELISLE EXPEEIENCE TABLES. 



Table XVII — (Continued). 

Age. Annuity. 


Single 
Premimn. 


32 


12.860 


.21547 


33 


12.771 


.22051 


34 


12.675 


.22594 


35 


12.573 


.23172 


36 


12.465 


.23783 


37 


12.354 


.24411 


38 


12.239 


.25062 


39 


12.120 


.25736 


40 


12.002 


.26404 


41 


11.890 


.27038 


42 


11.779 


.27666 


43 


11.668 


.28294 


44 


11.551 


.28957 


45 


11.428 


.29653 


46 


11.296 


.30400 


47 


11.154 


.31204 


48 


10.998 


.32087 


49 


10.823 


.33077 


50 


10.631 


.34164 


51 


10.422 


.35347 


52 


10.208 


.36558 


53 


9.988 


.37804 


54 


9.761 


.39089 


55 


9.524 


.40431 


56 


9.280 


.41812 


57 


9.027 


.43243 


58 


8.772 


.44687 


59 


8.529 


.46062 


60 


8.304 


.47336 


61 


8.108 


.48445 


62 


7.913 


.49549 


63 


7.714 


.50676 


64 


7.502 


.51875 


65 


7.281 


.53126 


66 


7.049 


. 54440 


67 


6.803 


.55832 



SINGLE LIFE ANNUITIES SINGLE PKEMIUMS. 169 



Table XVII— (Concluded). 



Age. 

68. 

69. 

70. 

71. 

72. 

73. 

74. 

75. 

76. 

77. 

78. 

79. 

80. 

81. 

82. 

83. 

84. 

85. 

86. 

87. 

88. 

89. 

90. 

91. 

92. 

93. 

94. 

95. 

96. 

97. 

98. 

99. 
100. 
101. 
102. 
103. 



Annuity. 


single 
Premium. 


6.546 


.57287 


6.277 


. 58809 


5.998 


.60389 


5.704 


.62053 


5.424 


.63638 


5.170 


.65075 


4.944 


.66355 


4.760 


.67396 


4.579 


.68421 


4.410 


.69377 


4.238 


.70351 


4.040 


.71472 


3.858 


.72502 


3.656 


.73645 


3.474 


.74675 


3.286 


.75740 


3.102 


.76781 


2.909 


.77874 


2.739 


.78836 


2.599 


.79628 


2.515 


.80101 


2.417 


.80658 


2.266 


.81513 


•2.248 


.81615 


2.337 


.81111 


2.440 


.80528 


2.492 


.80234 


2.522 


.80064 


2.486 


.80268 


2.368 


.80936 


2.227 


.81734 


2.004 


.82996 


1.596 


.85306 


1.175 


.87689 


0.744 


.90128 


0.314 


.92562 



170 



CAELISLE EXPERIENCE TABLES. 



Table XVKi- 



Two Lives ■ 
Columns. 



Commutation 



CAKnSLE Table of Mortality/, with Interest at 6^ 
Per Annum (Makehamized) . 



Equal p. 

Ages. '-'xx. 

10 2330240000 

11 2176390000 

12 2032220000 

13 1897160000 

14 1770510000 

15 1651860000 

16 1540590000 

17 1436280000 

18 1338490000 

19 1246720000 

20 1160710000 

21 1080130000 

22 1004500000 

23 933566000 

24 867000000 

25 803513000 

26 744540000 

27 689798000 

28 638966000 

29 591739000 

30 547904000 

31 507175000 

32 469367000 

33 434237000 

34 401625000 

35 371326000 

36 343185000 

37 317046000 

38 292763000 

39 270216000 

40 249267000 



32654970000 

30324730000 

28148340000 

26116120000 

24218960000 

22448450000 

20796590000 

19256000000 

17819720000 

16481230000 

15234510000 

14073800000 

12993670000 

11989175000 

11055609000 

10188609000 

9385096000 

8640556000 

7950758000 

7311795000 

6720056000 

6172152000 

5664977000 

5195610000 

4761373000 

4359748000 

3988422000 

3645237000 

3328191000 

3035428000 

2765212000 



TWO LIVES COMMUTATION COLUMNS. 



171 



Table XVIIT- 

Equal T-| 

Ages. '-'jrx. 

41 229805000 

42 .. . 211716000 

43 194925000 

44 179317000 

45 164822000 

46 151360000 

47 138856000 

48 127244000 

49 116459000 

50 106445000 

51 97149600 

52 88526800 

53 80528400 

54 73111000 

55 66239500 

56 59873100 

57 53986600 

58 48542200 

59 43518500 

60 38883700 

61 34619600 

62. 30701200 

63 27108900 

64 23824600 

65 20830500 

66 18109000 

67 15646100 

68 13427100 

69 11437600 

70 9664300 

71 8093640 

72 6712400 

73 5507980 

74 4467510 

75 , 3577670 

76 2825230 



(Continued). 

2515945000 

2286140000 

2074424000 

1879499000 

1700182000 

1535360000 

1384000000 

1245144000 

1117900000 

1001441000 

894996100 

797846500 

709319700 

628791300 

555680300 

489440800 

429567700 

375581100 

'327038900 

283520400 

244636700 

210017100 

179315900 

152207000 

128382400 

107551900 

89442900 

73796800 

60369700 

48932100 

39267800 

31174160 

24461760 

18953780 

14486270 

10908600 



172 



CAELISLE EXPEEIENCE TABLES. 



Table 



Equal 
Ages. 

77. 

78. 

79. 

80. 

81. 

82. 

83. 

84. 

85. 

86. 

87. 

88. 

89. 

90. 

91. 

92. 

93. 

94. 

95. 

96. 

97. 

98. 

99. 
100. 
101. 
102. 
103. 
104. 



XYIIl— (Concluded). 


D,,. 


N... 


2197300 


8083370 


1680600 


5886070 


1262110 


4205470 


929033 


2943366 


669029 


2014333 


470369 


1345304 


322131 


874935 


214372 


552804 


138236 


338432 


86126.4 


200196.7 


51678.5 


114070.3 


29755.3 


62391.8 


16376.4 


32636.5 


8578.90 


16260.10 


4257.62 


7681.20 


1991.59 


3423.58 


873.242 


1431.997 


356.689 


558.755 


134.822 


202.066 


46.8121 


67.2444 


14.8126 , 


20.43S3 


4.2338 


5.6197 


1.0827 


1.3859 


.2451 


.3032 


.0485 


.0581 


.0083 


.0096 


.0012 


.0013 


.0001 


.0001 



TWO LIVES ANNUITIES SINGLE PEEMIUMS. 173 



Table XIX — Two Lives. 

ANNUITIES AND SINGLE PREMIUMS PEE $1. 

CARLISLE Table of Mortality, with Interest at 6'4 
Per Annum (Makehamized) . 

Equal Single 

Ages. Annuity. Premium. 

10 13 . 0136 . 20675 

11 12.9335 .21128 

12 12.8510 .21598 

13 12.7659 .2207!) 

14 12.6791 .22572 

15 12.5898 .23075 

16 12.4991 .23591 

17 12.4069 .24111 

18 12.3133 .24643 

19 12.2197 .25170 

20 12.1252 .25708 

21 12.0297 .26245 

22 11.9355 .26777 

23 11.8423 .27310 

24 11.7516 .27819 

25 11.6801 .28226 

26 11.6052 .28651 

27 11.5262 '.29098 

28 11.4432 .29568 

29 11.3565 .30054 

30 11.2650 .30576 

31 11.1697 .31113 

32 11.0694 .31685 

33 10.9649 .32274 

34 10 . 8553 . 32897 

35 10 . 7410 . 33541 

36 10.6218 .34215 

37 10.4975 .34917 

3& 10.3682 .35653 

39 10.2333 .36417 

40 10,0934 .3720& 



174 



CARLISLE EXPERIENCE TABLES. 



Table XIX — (Continued). 

Equal Single 

Ages. Annuity. Premium. 

41 9.9482 .38030 

42 9.7981 .3^880 

43 9.6422 .39763 

44 9.4814 .40673 

45 9.3153 .41614 

46 9.1438 .42581 

47 8.9672 .43583 

48 8.7855 .44608 

49 8.5991 .45666 

50 8.4081 .46747 

51 8.2126 .47851 

52 8'. 0125 .48983 

53 7.8083 .50144 

54 7.6005 .51315 

55 7.3890 .52515 

56 7.1746 .53727 

57 6.9569 .55960 

58 6.7372 .56205 

59 6.5149 .57463 

60 6.2915 .58725 

61 6 . 0664 . 60004 

62 5.8407 .61277 

63 5.6147 .62557 

64 5.3886 .63836 

65 5.1632 .65115 

«6 4.9391 .66383 

67 4.7166 .67639 

'68 4.4961 .68891 

69 4.2782 .70125 

70 4.0632 .71341 

71 3.8517 .72536 

72 3.6443 .73713 

73 3.4411 .74862 

74 3.2426 .75983 

75 3.0491 .77081 

76 2.8611 .78146 



TWO LIVES ANNUITIES SINGLE PREMIUMS. 175 



Equal 
Ages. 


Table XIX — (Concluded). 

Annuity. 


single 
Premium. 


77.... 


2.6788 


.79175 


78.... 


2.5024 


.80178 


79.... 


2.3321 


.81140 


80 


2.1682 


.82068 


81 


2.0108 


.82956 


82 


1.8601 


.83811 


83 


1.7161 


.84626 


84.... 


1.5787 


.85402 


85 


1.4482 


.86144 


86.... 


1.3245 


.86840 


87.... 


1.2073 


.87507 


88.... 


1-.0968 


.88130 


89.... 


.9929 


.88719 


90 


.8954 


.89274 


91 


.8041 


.89788 


92 


.7190 


.90270 


93 


.6399 


.90717 


94 


.5665 


.91130 


95. . . 


.4988 


.91515 


96. . . 


.4365 


.91866 


97.... 


.3794 


.92194 


98 


.3273 


.92488 


99 


.2800 


.92755 


100 


.2370 


.92998 



176 



CARLISLE EXPERIENCE TABLES. 



Table XX — Three LavEs — Commutation 

Columns. 

CAELISIE Table of Mortality, with Interest at Q^ 
Per Annum (Makehamised). 

194:31&9000000000 

1792656000000000 

1652766000000000 

1522812000000000 

1402129000000000 

1290lil000000000 

1186178400000000 

1089800800000000 

1000478400000000 

917746400000000 

841176400000000 

770358600000000 

704906000000000 

644470700000000 

588721900000000 

537353100000000 

490167100000000 

446835200000000 

407050800000000 

370533700000000 

337027200000000 

306291400000000 

278109000000000 

252276800000000 

228610100000000 

206936500000000 

187099100000000 

168952300000000 

152362400000000 

137206300000000 

123369700000000 

110748100000000 



Equal 
Ages. 


D^^^. 


10 


150533000000000 


11 


139890000000000 


12 


129954000000000 


13 


120683000000000 


14 


112018000000000 


15 


103933000000000 


16 


96377600000000 


17 


89322400000000 


18 


82732000000000 


19 


76570000000000 


20 


70817800000000 


21 


65452600000000 


22 


60435300000000 


23 


55748800000000 


24 


51368800000000 


25 


47186000000000 


26 


43331900000000 


27 


39784400000000 


28 


36517100000000 


29 


33506500000000 


30 


30735800000000 


31 


28182400000000 


32 


25832200000000 


33 


23666700000000 


34 


21673600000000 


35 


19837400000000 


36 


18146800000000 


37 


165S9900000000 


38 


15156100000000 


39 


13836600000000 


40 


12621600p00000 


41 


11503000000000 



THREE LIVES COMMUTATION COLUMNS. 177 



Equal 
Ages. 


Table XX — 


• (Continued). 

^xxx. 


42 


10472600000000 


99245100000000 


43 


9525280000000 


88772560000000 


44 


8652900000000 


79247280000000 


45 


.7850660000000 


70594380000000 


46 


7112950000000 


62743720000000 


47 


6434790000000 


55630770000000 


48 


5811630000000 


49195980000000 


49 


5239060000000 


43384350000000 


50 


4713430000000 


38145290000000 


51 


4231170000000 


33431860000000 


52 


3789350000000 


29200690000000 


53 


3384770000000 


25411340000000 


54 


3014620000000 


22026570000000 


55 


2676620000000 


19011950000000 


56 


2368170000000 


16335330000000 


57 


2087600000000 


13967160000000 


58 


1832530000000 


11879560000000 


59 


1601530000000 


10047030000000 


60 


1392610000000 


8445500000000 


61 


1204510000000 


7052890000000 


62 


1035660000000 


5848380000000 


63 


884710000000 


4812723000000 


64 


750455000000 


3928013000000 


65 


631669000000 


3177558000000 


66 


527149000000 


2545889000000 


67 


435870000000 


2018740000000 


68 


356756000000 


1582S70000000 


69 


288772000000 


1226114000000 


70 


230919000000 


937342000000 


71 


182211000000 


706423000000 


72 


141686000000 


524212000000 


73 


108431000000 


382526000000 


74 


81548500000 


274095400000 


75 


60168600000 


192546900000 


76 


43471400000 


132378300000 


77 


30697900000 
12 


88906900000 



178 



CAELISLE EXPERIENCE TABLES. 





Table XX — (Concluded). 


Equal 
Ages. 


D^^^. 


N.... 


78 


21140900000 


58209000000 


79 


14165300000 


37068100000 


80 


9210460000 


22902830000 


81 


5795030000 


13692370000 


82 


3517220000 


7897340000 


83 


2052310000 


4380120000 


84 


1147090000 


2327810000 


85 


611550000 


1180725000 


86 


309639000 


569175000 


87 


148173000 


259536000 


88 


66650600 


111363000 


89 


28018100 


44712400 


90 


10937400 


16694300 


91 


• 3937020 


5756940 


92 


1296790 


1819920 


93 


387637 


523137 


94 


104186 


135500 


95 


24927.1 


31314 


96 


5250.71 


6386.93 


97 


962.235 


1136.226 


98 


151.382 


173.991 


99 


20.1553 


22.6091 


100 


2.2354 


2.4538 


101 


. 2028 


.2184 


102 


.0148, 


.0156 


103 


.0008 


.0008 



THREE LIVES ANNUITIES SINGLE PKEMIUMS. 179 



Table XXI — Three Lives. 

ANNUITIES AND SINGLE PREMIUMS PEE $1. 

CARLISLE Table of Mortality, with Interest at 6^ 
Per Annum (Makehamized) . 

Bqual 



10. 

11. 

12. 
13. 
14. 
15. 
16. 
17. 
18. 
19. 
20. 
21. 
22. 
23. 
24. 
25. 
26. 
27. 
28. 
29. 
30. 
31. 
32. 
33. 
34. 
35. 
36. 
37. 
38. 
39. 
40. 



Annuity. 


single 
Premium. 


11.9087 


.26930 


11.8148 


.27463 


11.7181 


.28012 


11.6183 


.38578 


11.5170 


.29149 


11.4129 


.29738 


11.3076 


.30332 


11.2008 


.30937 


11.0930 


.31549 


10.9857 


.32155 


10.8780 


.32766 


10.7697 


.33377 


10.6638 


.33977 


10.5603 


.34566 


10.4607 


.35126 


10.3880 


.35540 


10.3119 


.35970 


10.2314 


.36428 


10.1469 


.36903 


10.0586 


.37402 


9.9653 


.37934 


9.8682 


.38483 


9.7660 


.39060 


9.6596 


.39660 


9.5479 


.40295 


9.4316 


.40951 


9.3103 


.41642 


9.1840 


.42354 


9.0529 


.43096 


8.9162 


. 43872 


8.7745 


.44670 



180 



CAELISLE EXPERIENCE TABLES. 



Equal 



Tabi^ XXI — (Continued). 



41. 
42. 
43. 
44. 
45. 
46. 
47. 
48. 
49. 
50. 
51. 
52. 
53. 
54. 
55. 
56. 
57. 
58. 
59. 
60. 
61. 
62. 
63. 
64. 
65. 
66. 
67. 
68. 
69. 
70. 
71. 
■72. 
73. 
74. 
75. 
76. 



Annuity. 

8 . 6278 
8.4766 
8.3197 
8.1585 
,9922 
,8211 
.6453 
.4651 
,2809 
.0929. 
,9013 
6.7060 
6.5076 
6.3066 
6.1030 
5.8979 
5.6905 
5.4826 
5.2734 
5.0645 
4.8554 
4.6470 
4.4399 
4.2342 
4.0304 
3.8295 
3.6315 
3.4368 
3.2460 
3.0592 
2.8770 
2.6998 
2.5278 
2.3611 
2.2001 
2.0452 



Single 
Premium. 

.45502 

.46356 

.47245 

.48157 

.49102 

.50069 

.51066 

.52085 

.53126 

.54191 

.55277 

.56381 

.57502 

.58639- 

.59794 

.60955 

. 62126 

.63304 

. 64492 

.65670 

.66859 

.68035 

.69208 

.70373 

.71528 

.72660 

.73781 

.74885 

.75966 

.77024 

.78054 

.79057 

.80030 

.80975 

.81887 

. 82764 



THKEE LIVES ANNUITIES SINGLE PREMIUMS. 181 



Bquai 



Table :KX1— {Concluded). 



77. 
78. 
79. 
80. 
81. 
82. 
83. 
84. 
85. 
86. 
87. 
88. 
89. 
90. 
91. 
92. 
93. 
M. 
95. 
96. 
97. 
98. 
99. 
100. 



Annuity. 


Single 
Premium. 


1 


.8962 


.83608 


1 


.7534 


.84417 


1 


.6168 


.85186 


1 


.4866 


.85922 


1 


.3628 


.86625 


1 


.2453 


.87293 


1 


.1342 


.87920 


1 


.0293 


.88515 




.9307 


.89069 




.8382 


.89597 




.7516 


.90083 




.6708 


.90541 




.5958 


.90966 




.5264 


.91362 




.4623 


.91725 




.4034 


.92058 




.3496 


: 92358 




.3006 


.92636 




.2562 


.92891 




.2164 


.93117 




.1808 


.93315 




.1494 


.93496 




.1217 


.93649 




.0977 


.93785 



182 COMBINED OE ACTU ABIES ' EXPERIENCE TABLES. 

Table XXII. 
COMBINED EXPERIENCE Table of Mortality. 

Age. 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

31 

32 

33 

34 

35 

36 

37 

38 

39 

40 

41 

42 



Ix 


dx 


tation. 


00,000 


676 


48.36 


99,324 


674 


47.68 


98,650 


672 


47.01 


97,978 
97,307 
96,636 


671 
671 
671 


46.33 
45.64 
44.96 


95,965 


672 


44.27 


95,293 


673 


43.58 


94,620 
93,945 
93,268 


675 
677 
680 


42.88 
42.19 
41.49 


92,588 


683 


40.79 


91,905 


686 


40.09 


91,219 


690 


39.39 


90,529 


694 


38.68 


89,835 


698 


37.98 


89,137 


703 


37.27 


88,434 


708 


36.r,n 


87,726 
87,012 
86,292 


714 

720 
727 


3"').sr, 

35.15 
34.43 


85,565 


734 


33.72 


84,831 


742 


33.01 


84,089 


750 


32.30 


83,339 


758 


31.58 


82,581 


767 


30.87 


81,814 


776 


30.15 


81,038 


785 


29.44 


80,253 


795 


28.72 


79,458 


805 


28.00 


78,653 
77,838 
77,012 


815 
826 
839 


27.28 
26.56 
25.84 



COMBINED EXPEEIENCB MORTALITY TABLE. 183 



Table XXII — (Continued). 

Age. ix dx 

43 . 76,173 857 

44 75,316 881 

45 • ' 74,435 909 

46 73,526 944 

47 72,582 981 

48 71,601 1,021 

49 70,580 1,063 

50 69,517 1,108 

51 68,409 1,156 

52 67,253 1,207 

53 66,046 1,261 

54 64,785 1,316 

55 63,469 1,375 

56 62,094 1,436 

57 60,658 1,497 

58 59,161 1,561 

59 57,600 1,627 

60 55,973 1,698 

61... 54,275 1,770 

62 52,505 1,844 

•63 50,661 1,917 

64 48,744 1,990 

65 46,754 2,061 

66 44,693 2,128 

67 '. 42,565 2,191 

68 40,374 2,246 

69 38,128 2,291 

70 • 35,837 2,327 

71 33,510 2,351 

72 31,159 2,362 

73 28,797 2,358 

74 26,439 2,339 

75 24,100 2,303 

76 21,797 2,249 

77 • • 19,548 2,179 

78 17,369 2,092 



Expec- 
tation. 


25. 


12 


24. 


40 


23. 


69 


22. 


97 


22. 


27 


21. 


56 


20. 


87 


20. 


18 


19. 


50 


18. 


82 


18. 


16 


17. 


50 


16. 


86 


16. 


,22 


15. 


59 


14. 


,97 


14. 


,37 


13, 


.77 


13, 


,18 


12, 


,61 


12, 


,05 


11, 


.51 


10 


.97 


10 : 


:46 


9 


.96 


9 


.47 


9 


.00 


8 


.54 


8 


.10 


7 


.67 


7 


.26 


6 


.86 


6 


.48 


6 


.11 


5 


.76 


5 


.42 



184 COMBINED OB ACTUARIES' EXPEBIBNCB TABLES. 

Table XXII — (Concluded). 

Expeo 

Age. Ix ux tation. 

79 15-,277 1,987 5.09 

80 13,290 1,866 4.78 

81 11,424 1,730 4.48 

82 9,694 1,582 4.18 

83 8,112 1,427 3.90 

84 ' 6,685 1,268 3.63 

85 5,417 1,111 3.36 

8Q 4,306 958 3.10 

87 3,348 811 2.84 

88 2,537 673 2.59 

89 1,864 545 2.35 

90 , 1,319 427 2.11 

91 892 322 1.89 

92 570 231 1.67 

93 339 155 1.47 

94 184 95 1.28 

95 89 52 1.12 

96 37 24 .99 

97 13 9 .89 

98 4 3 .75 

99 1 1 .50 



SINGLE LIFE COMMUTATION COLUMNS. 



185 



Table XXIII- 



■Single Life- 
Columns. 



Commutation 



COMBINED EXPEEIENCE Table of Mortality, with 
Interest at 4^ Per Annum. 



ige. 


D.. 


N.. 


M 


X. 


10.. 


67556 


.41688 


1381771 


.33883 


14411 


.36539 


11.. 


64518 


.97645 


1314214 


.92194 


13972 


.24868 


12.. 


61616 


.49894 


1249695 


.94550 


13551 


.27027 


13.. 


58843 


.04781 


1188079 


.44656 


13147 


.-68448 


14.. 


56192 


.36788 


1129236 


.39875 


12760 


.19870 


15.. 


53658 


. 54048 


1073044 


.03086 


12387 


.61622 


16.. 


51236 


.49808 


1019385 


.49038 


12029, 


.36383 


17.. 


48920 


.87672 


968148 


.99230 


11684, 


.37701 


18.. 


46707 


.09281 


919228 


.11558 


11352, 


. 16529 


19.. 


44590 


.28253 


872521, 


.02277 


11031, 


.78165 


20.. 


42566 


.29770 


827930 


. 74024 


10722, 


.80769 


21.. 


40630, 


.72555 


785364.44255 


10424, 


.40084 


22.. 


38779, 


.80981 


744733, 


.71699 


10136, 


.20531 


23.. 


37009, 


,95040 


705953. 


.90718 


9857. 


.87705 


24.. 


35317, 


,30695 


668943, 


,95678 


9588. 


,69323 


25.. 


33698, 


.61793 


633626, 


,64983 


9328. 


.36217 


26.. 


32150. 


,75616 


599928. 


,03190 


9076. 


60108 


27.. 


30670. 


,37656 


567777. 


,27575 


8832. 


,78903 


28.. 


29254. 


, 64466 


537106. 


,89918 


8596. 


68698 


29.. 


27900. 


52090 


507852. 


,25454 


8367. 


,74187 


30.. 


26605. 


,43450 


479951. 


,73364 


8145. 


,75243 


31.. 


25366. 


62195 


453346. 


29915 


7930. 


,22583 


32.. 


24181. 


75011 


427979. 


67720 


7720. 


99330 


33.. 


23048. 


,30493 


403797. 


92708 


7517. 


61542 


34.. 


21964. 


16759 


380749. 


62216 


7319. 


,95135 


35.. 


20927. 


30299 


358785. 


45457 


7127. 


86243 


36.. 


19935. 


,51281 


337858. 


15158 


6940. 


96852 


37.. 


18986. 


94796 


317922. 


,63877 


6759. 


15416 


38.. 


18079. 


83167 


298935. 


,69081 


6582. 


30510 


39.. 


17212. 


,24015 


280855. 


85914 


6410. 


09172 


40.. 


16382. 


55823 


263643. 


61899 


6242. 


41904 



186 COMBINED OB ACTUAKIEs' EXPEBIENCB TABLES. 



Table XXIII — (Continued). 



Age. 


D 


'x. 


N, 




M,. 


41. . 


15589 


.23^33 


.247261 


.06076 


6079.19253 


42. . 


14830 


.58054 


231671 


. 82743 


5920.12563 


4d.. 


14104 


.81747 


216841 


.24690 


5764.76951 


44.. 


13409 


.73877 


202736 


.42943 


5612.18379 


45.. 


12743 


.15379 


189326, 


.69066 


5461.35799 


46.. 


12103 


.39849 


176583 


.53687 


5311.72400 


47.. 


11488 


. 46443 


164480, 


.13838 


5162.30526 


48.. 


10897 


.29735 


152991 


.67395 


5013.00220 


49. 


10328 


.75625 


142094, 


.37660 


4863.58792 


50. . 


9781 


.91888 


131765, 


.62035 


4714.01040 


St.. 


9255 


.77818 


121983, 


.70147 


4564.09735 


52.. 


8749 


.39490 


112727, 


.92330 


4413.70554 


53.. 


8261, 


. 89245 


103978, 


. 52840 


4262.71828 


54.. 


7792, 


.45209 


95716, 


.63595 


4111.04302 


55.. 


7340, 


.53974 


87924. 


,18386 


3958.84036 


56. . 


6905, 


.30136 


80583. 


, 64411 


3805.93043 


57.. 


6486, 


.16133 


73678, 


.34276 


3652.37892 


58.. 


6082. 


.77604 


67192, 


,18143 


3498.46137 


59. . 


5694. 


.49826 


61109. 


,40538 


3344.13652 


60. . 


5320, 


.81583 


55414, 


,90712 


3189.47324 


61. 


4960. 


96468 


50094. 


09129 


3034.26886 


62. 


4614, 


,59537 


45133. 


,12661 


2878.70589 


63. 


4281. 


,27754 


40518. 


,53124 


2722.87249 


64. 


3960. 


,84138 


36237. 


25370 


2567.10085 


65.. 


3653. 


,01721 


32276. 


41233 


2411.61673 


66.. 


3357. 


67853 


28623. 


39512 


2256.77872 


67.. 


3074. 


S1439 


25265. 


71659 


2103.05600 


68. . 


2804. 


,36609 


22190. 


90220 


1950.869P5 


69.. 


2546. 


49961 


19386. 


53611 


1800.86360 


70. 


2301. 


43067 


16840. 


03651 


1653.73695 


71.. 


2069. 


22319 


14538. 


60584 


1510.04605 


72.. 


1850. 


04836 


12469. 


38265 


1370.45672 


73.. 


1644. 


04416 


10619. 


33428 


1235.60822 


74.. 


1451. 


36925 


8975. 


29013 


1106.16578 


75.. 


1272. 


08636 


7523. 


92088 


982.70479 


76.. 


1106. 


27459 


6251. 


83452 


865.81942 





SIHGLE LIFE — 


COMMUTATION COLUMNS. lo/ 




Table XXISI— (Concluded) 


, 


A«e. 


D.. 


N., 


M:,. 


77.. 


953.97107 


5145.55993 


756.06492 


78.. 


815.03142 


4191.58886 


653.81646 


79.. 


689.29364 


3376.55745 


559.42605 


80.. 


576.57769 


2687.26380 


473.22139 


81. . 


476.56014 


2110.68611 


395.37990 


82. . 


388.83844 


1634.12597 


3^.98744 


83.. 


312.86774 


1245.28753 


264.97206 


84.. 


247.91392 


932.41979 


212.05162 


85.. 


193.16347 


684.50587 


166.83632 


S6.. 


147.64096 


491.34241 


128.74317 


^'7.. 


110.37861 


343.70145 


97.15933 


■^s. 


80.42417 


233.-32284 


71.45022 


■^9. . 


56.81705 


152.89866 


50.936-34 


00.. 


38.65843 


96.081C1 


34.96299 


en. . 


25.13801 


57.42318 


22.92943 


92.. 


15.44570 


32.28516 


14.20396 


93.. 


8.83282 


16.83946 


8.18514 


94.. 


4.60982 


8.00665 


4.30187 


95.. 


2.14399 


3.39683 


2.01334 


96.. 


.85704 


1.25284 


.80885 


n7. . 


.28954 


.39580 


.27432 


98.. 


.08566 


.10625 


.08158 


99.. 


.02059 


.02059 


,01980 



188 COMBINED OK ACTUARIES ' EXPEEIENCE TABLES. 



Table XXIV — Single Life. 

ANNUITIES AND SINGLE PREMIUMS PEE $1. 

COMBINED EXPERIENCE Table of Mortality, with 
Interest at 4^ Per Annum. 

Single 

Age. ^ Annuity. Premium. 

10 19.454 .2133:2 

11 19.369 .216o(; 

12 19.282 .21993 

13 19.191 .22344 

14 19.096 .22708 

15 18.998 .23086 

16 18.896 .23478 

17 18 . 790 . 23884 

18 18.681 .24305 

19 18.568 .24740 

20 18.450 .25191 

21 18.329 .25656 

22 18 . 204 . 26138 

23 18.075 .26636 

24 17.941 .27150 

25 17.803 .27682 

26 17.660 .28231 

27 17.512 .28799 

28 17.360 .29386 

29 17.202 .29991 

30 17.040 .30617 

31 16.872 .31262 

32 16.698 .31929 

33 16.520 .32617 

34 16.335 .33327 

35 16.144 .34060 

36 15 . 948 . 34817 

37 15.744 .35599 

38 15.534 .36407 

39 15.317 .37241 

40 15.093 .38104 



SINGLE LIFE ANNUITIES SINGLE PBEMIUMS. 189 



Table XXIV — (Continued). 

Single 

Age. Annuity. Premium. 

41 14.861 .38996 

42 14.621 .39918 

43 14.374 .40871 

44 14.119 .41852 

45 , 13.857 .42857 

46 13 . 590 . 43886 

47 13.317 .44935 

48 13.039 .46002 

49 12.757 .47088 

50 12.470 .48191 

51 12.179 .49311 

52 '. 11.884 .50446 

53 11.585 .51595 

54 11.283 .52757 

55 10.978 .53931 

56 10.670 .55116 

57 10.359 .56310 

58 10 . 046 . 57514 

59 9.731 .58726 

60 ; 9.415 .59943 

61 9.098 .61163 

62 8.781 .62383 

63 8.464 .63600 

64 8.149 .64812 

65 7.836 .66017 

66 7.525 .67212 

67 7.217 .68396 

68 6.913 .69565 

69 6.613 .70719 

70 6.317 .71857 

71 6.026 .72976 

72 5.740 .74077 

73 5.459 .75157 

74 5.184 .76215 

75 4.915 .77251 

76 4.651 .78264 



190 COMBINED OE ACTU ABIES ' EXPERIENCE TABLES. 



Table XX.W — (Concluded). 

Single 

Age. Annuity. Premium. 

77 4.394 .79254 

78 4.143 .80220 

79 3.899 .81159 

80 3.661 .82074 

81 3.429 .82965 

82 3.203 .83836 

83 2.980 .84691 

84 2.761 .85534 

85 2.544 .86371 

86 2.328 .87200 

87 2.114 .88024 

88 1.901 .88842 

89 1.691 .89650 

90 1.485 .90441 

91 1.284 .91214 

92 1.090 .91961 

93 0.906 .92667 

94 0.737 .93320 

95 0.584 .93906 

96 0.462 .94378 

97 0.367 .94742 

98 O.240 .95229 



TWO lilVES ANNUITIES ■ 



SINGLE PEEMIUMS. 



191 



Table XXV — Two Lives. 

ANNUITIES AND SINGLE PEEMIUMS FEB $1. 

COMBINED EXPERIENCE Table of Mortality, with 
Interest at 4;^ Per Annum. 

Agbs. Single 

Older. Younger. Annuity. Premium. 

10 10 16.832 .31415 

11 11 16.744 .31754 

12 12 16.652 .32107 

13 13 16.556 .32477 

14 14 16.456 .32862 

15 10 16.578 .32392 

15 16.353 .33257 

16 11 16 . 480 . 32769 

16 16.246 .33669 

17 12 16.378 .33161 

17 16.135 .34096 

18 13 16.272 .33569 

18 16.020 .34538 

19 14 16.162 .33992 

19 15.901 .34996 

20 10 16.243 .33680 

15 16.048 .34431 

20.. 15.778 .35469 

21 11 16.133 .34103 

16 15.930 .34885 

21 15.651 .35958 

22 12 16.018 .34546 

17... 15.808 .35354 

22 15.520 .36462 

23 13 15.899 .35003 

18 15.682 .35838 

23 15.384 .36985 

24 14 15.776 .35477 

19 15.552 .36338 

24 15.244 .37523 



192 COMBINED OE ACTUARIES' EXPERIENCE TABLES. 





Table XXV— (( 


Continued). 






Ages. 




Single 


Older. 


Younger. 


Annuity. 


Premium. 


25 


10 


15.811 


.35342 




15 


15.649 


.35965 




20 


15.417 


.36858 




25 


15.100 


.38077 


26 


11 


15.685 


.35827 




16 


15.517 


.36473 




21 


15.278 


.37392 




26 


14.951 


.38650 


27 


12 


15.554 


.36331 




17 


15.381 


.36996 




22 


15.134 


. 37947 




27 


14.797 


.39242 


28 


13 


15.419 


.36850 




18 


15.240 


.37538 




23 


14.986 


.38515 




28 


14.638 


.39854 


29 


14 


15.279 


.37388 




19 


15.094 


.38100 




24 


14.833 


.39103 




29 


14.474 


.40485 


30 


10 


15.270 


.37423 




15 


15.134 


.37947 




20 


14.944 


.38677 




25 


14.675 


.39712 




30 


14.305 


.41135 


31 


11 


15.125 


.37981 




16 


14.984 


.38523 




21 


14.789 


.39273 




26 


14.512 


.40338 




31 


14.131 


.41804 


32 


12 


14.975 


.38558 




17 


14.829 


.39119 




22 


14.629 


.39888 




27 


14.344 


.40985 




32 


13.952 


.42492 


33 


13 


14.819 


.39157 



TWO LIVES ANNUITIES SINGLE PREMIUMS. 193 



Table XXV — (Continued). 

Ages. Single 

Older. Youiiger. Annuity. Premium. 

33 18 14.6C9 .39734 

23 14.464 .40523 

28 14.171 .41650 

33 13.767 .43204 

34 14 14.658 .39777 

19 ..., 14.504 .40370 

24 14.294 .41177 

29 13.992 .42338 

34 13.577 .43935 

35 10 14.600 .40000 

15 14.491 .40419 

20 14.333 .41026 

25 14.118 .41854 

30 13.808 .43046 

35 13.381 .44688 

36 11 14.431 .40650 

16 14.318 .41084 

21 14.157 .41704 

26 13.936 '.42554 

31 13.618 .43777 

36 13.178 .45469 

37 12 14.255 .41327 

17 14.139 41773 

22 13.975 .42404 

27 13.749 .43273 

32 13.422 .44530 

37 12.969 .46273 

;18 13 14.073 42026 

18 13.954 .42485 

23 13.787 .43127 

28 13.555 .44019 

33 13.220 .45308 

38 12.753 .4710.T 

;59 14 13.884 .427r,4 

19 13.763 .43210 

24 13.592 .43877 

13 



194 COMBINED OE ACTXJAEIES* EXPERIENCE TABLES. 



Table XXV— (Continued). 

AoBS. single 

Older. Younger. Annuity. Premium. 

39 29 ; 13.355 .44789 

34 13.011 .46111 

39 12.530 .47962 

40 10 13.772 .43184 

15 13.688 .43507 

20 13.565 .43981 

25 13.391 .44650 

30 13.148 .45584 

35 12.795 .46943 

40 12.299 .48850 

41 11 13.571 .43958 

16 13.485 .44289 

21 13.360 .44769 

26 13.183 .45450 

31 12.934 .46408 

36 12.572 .47800 

41 12.060 .49769 

42 12 13.363 .44757 

17 13.275 .45096 

22 13.148 .45584 

27 12.968 .46277 

32 12.713 .47257 

37 12.342 .48684 

42 11.813 .50719 

43 13 13.147 .45588 

18 13.057 .45935 

23 12.928 .46431 

28 12.745 .47135 

33 12.485 .48135 

38 12.104 .49600 

43 11.558 • .51700 

44 14 12.924 .46447 

19 12.832 .46800 

24 12.702 .47300 

29 12.516 .48015 

34 12.250 .49038 



TWO LIVES ANNUITIES SINGLE PREMIUMS. 195 



Table XXV — {Continued). 

Aqbs. Single 

Older. Younger. Annuity. Premium. 

44 39 11.859 .50542 

44 11.295 .52715 

45 10 12.761 .47073 

15 12.695 .47327 

20 12.601 .47688 

25 12.470 .48192 

30 12.281 .48919 

35 12.009 .49965 

40 11.607 .51511 

45 11.027 .53742 

46 11 12.527 .47973 

16 12.460 .48231 

21 12.364 .48600 

26 12.232 .49107 

31 12.040 .49846 

36 11.762 .50915 

41 11.349 .52503 

46 10.753 .54796 

47 12 12.288 .48892 

17 12.219 .49157 

22 12.123 .49520 

27 11.989 .50042 

32 11.794 .50793 

37 11.510 .51885 

42." 11.085 .53519 

47 10.476 .55862 

48 13 12.043 .49834 

18 11.974 .50100 

23 11.877 .50473 

28 11.741 .50996 

33 11.544 .51754 

38 11.253 .52873 

43 10.815 .54558 

48 10.196 .56939 

49 14 11.794 .50793 

19 11.724 .51062 



196 COMBINED OE ACTUAKIES' EXPEEIENCE TABLES. 



Table XXV — {Continued). 

Ages. Single 

Older. Younger. An.iuity. Premium. 

49 24 11.626 .51439 

29 11.489 .51965 

34 , 11.289 .52734 

39 10.991 .53881 

44 10.540 .55615 

49 9.913 .58026 

50 10 11.588 .51584 

15 11.540 .5176!) 

20 11.469 .52042 

25 11.371 .52419 

30 11.233 .52950 

35 11.030 .53731 

40 10.724 .54908 

45 10.261 .56688 

50 9.627 .59127 

51 11 11.330 .52577 

16 11.281 .52765 

21 11.210 .53038 

26 11.112 .53415 

31 10.973 .53950 

36 10.766 .54746 

41 10.452 .55954 

46 9.978 .57777 

51 9.339 .60234 

52 12 11.068 .53584 

17 11.018 .53776 

22 10.947 .54050 

27 10.849 .54427 

32 10.708 .54969 

37 10.498 .55777 

42 10.175 .57019 

47 9.693 .58873 

52 9.049 .61350 

53 13 10.801 .54611 

18 10.751 .54804 

23 10.680 .55077 



TWO LIVES ANNUITIES SINGLE PREMIUMS. 197 



Table XXV— (Continued). 

Ages. Single 

Older. Younger. Annuity. Premium. 

53 28...' 10.582 .55454 

33 10.440 .56000 

38 10.220 .56823 

43. _ 9.894 .58100 

48 9.405 .59981 

53 8.758 .6246!) 

54 14 10.531 .55650 

19 10.481 .^55842 

24 10.410 .56115 

2'9 10.312 .56492 

34 10.169 .57042 

39 9.950 .57885 

44 9.609, .59196 

49 9.116 .61092 

54 8.466 .63592 

55 10 10.294 .56562 

15 10.257 .56704 

20 10.207 .56896 

25 10.136 .^7169 

30 10.038 .57546 

35 9.894 .58100 

40 9.671 .58958 

45 , 9 . 321 . 60304 

50 8.825 .62212 

55 8.174 .64716 

56 11 10.017 .57627 

16 9.980 ,57769 

21 9.930 .57961 

26 9.859 .5823-1 

31 9.761 .58611 

36 9.616 .59169 

41 9.388 .60046 

46 9.031 .61419 

51 8.533 .63334 

56 7.882 .85888 

57 12 9.737 .58704 



198 COMBINED OB ACTUARIES' EXPERIENCE TABLES. 



Table XXV- 

Ages. 
Older. Younger. 


- (Continued). 

Annuity. 


Single 
Premium. 


57 17 


9.700 


.58846 


22 


9.650 


.59038 


27 


9.580 


.59308 


32 


9.482 


.59684 


37 


9.336 


. 60246 


42 


9.102 


. 61146 


47 


8.740 


.62538 


/ 52 


8.241 


. 64458 


57 


7.590 


.66962 


58 13 


9.454 


.59793 


18 


9.417 


.59935 


23 .... 


9 367 


.60127 


28 


9.299 


.60388 


3;; 


9.200 


.60769 


38 


9 . 052 


. 61338 


43 


8.813 


62257 


4S 


8.447 


. 63665 


53 


7.948 
7.298 


.65584 


58 


.68084 


59 1+ 


9.168 


. 60892 


19 


9.131 


.61034 


24 


9.082 


. 61223 


29 


9.014 


.61485 


34 


8.916 


. 61862 


39 


8.766 


.62439 


44 


8.521 


.63381 


49 


8.154 


. 64793 


54 


7.655 


. 66712 


59 


7.007 


.69204 


60 10 


8.905 


. 61904 


15 


8.880 


.62000 


20 


8.844 


.62139 


25 


8.795 


.62327 


30 


8 . 728 


.62584 


35 


8 . 630 


.62962 


40 


8.477 


.63550 



TWO LIVES ANNUITIES - 


- SINGLE PREMIUMS. 199 


Older. 


Table XXV — 

Ages. 

Younger. 


- (Continued). 

Annuity. 


Single 
Premium. 


60 


45 


8.227 


.64:511 




50 


7 . &60 


. 65923 




55 


7.362 


.67838 




60 


6.717 


.70319 


«1 


11 


8 615 


63019 




16 


8.590 


.63115 




21 


8.555 


.63250 




26 


8.507 


.63435 




31 


8.440 


.63692 




36 


8.343 


.64065 




41 


8.187 


.64665 




46 


7.933 


.65642 




51 


7.566 


.67054 




56 


7.071 


.68958 




61 


6.429 


.71427 


62 


12 


8.325 


.64135 




17 


8.300 


.64231 




22 


8.265 


.64366 




27 


8.218 


. 64546 




32 


8.152 ' 


.64800 




37 


8.055 


.65173 




42 


7.896 


.65785 




47 


7.639 


.66773 




52 


7.274 


.68177 




57 


6.782 


.70069 




62 


6 . 145 


.72519 


63 


13 


8.035 


.65250 




18 


8 . 010 


.65346 


• 


23 


7.976 


.65477 




28 


7.930 


.65654 




33 


7.865 


.65904 




38 


7.767 


.66281 




43 


7.605 


.66904 




48 


. . ■ 7.347 


. 67896 




53 


6.984 


.69293 




58 


6.495 


.71173 



200 COMBINED OK ACTUAEIES' EXPEKIENCB TABLES. 

Table XXV — (Continued). 

Ages. Single 

Older. Tounger. Annuity. Premium. 

63 63 5.864 .73600 

64 14 7.745 .66366 

19 7.720 .6646ii 

24 7.687 .66588 

29 7.641 .66765 

34 7.577 ,67011 

39 7.479 .67388 

44 7.313 .68026 

49 7.056 .69015 

54 6.696 .70400 

59 6.210 .72269 

64 5.588 .74661 

65 10 7.473 .67411 

15 7.456 .67477 

20 7.432 .67569 

25 7.399 .67696 

30 7.354 .67870 

35 7.291 .68111 

40 7.192 .68492 

45 7.024 .69139 

50 6.768 .70123 

55 6.410 .71500 

60.. 5.929 .73350 

65 5.317 .75704 

66 11 7.185 .68519 

16 7.168 .68584 

21 7.145 .68673 

26 7.113 .68796 

31 7.069 .68965 

36 7.007 .69204 

41 6.907 .69588 

46 6.736 .70246 

51 6.482 .71223 

56 6.129 .72580 

61 5.653 .74411 

66 5.051 .76727 



TWO LIVES — ANNUITIES SINGLE PREMIUMS. 201 



Table XXV — {Continued). 

AQE3. einsle 

Older. Younger. Annuity. Premium. 

61 12 6.900 ,69615 

17 6.883 .69680 

22 6.860 .69769 

27 6.829 .69888 

32 6.786 .70054 

37 6.725 .70289 

42 6.623 .70680 

47 6.451 .71342 

52 6.200 ,72308 

57 5.851 .73650 

62 5.381 .75458 

67 4.792 .77723 

68 13 6.617 .70704 

18 6.601 .70765 

23 6.578 .70854 

28 6.548 .70969 

33 6.507 .71127 

38 6.445 .71366 

43 6.342 .71761 

48' 6.170 .72423 

53 5.922 .73377 

58 5.578 .74700 

63 5.114 .76485 

68 4.539 .78696 

89 14 6.337 .71781 

19 6.321 .71842 

24 6.300 .71923 

29 6.270 .72038 

34 6.230 .72192 

39 6.169 .72427 

44 6.063 .72834 

49 5.893 .73488 

54 5.649 .74427 

59 5.309 .75734 

64 4.854 .77485 

69 4.293 .79642 



202 COMBINED OR ACTU ABIES ' EXPEKIENCE TABLES. 



Table XXV — (Continued). 

Ages. Single 

Older. Younger. Annuity. Premium. 

70 10 6.071 .72804 

15 6.061 .72842 

I'0 6.045 .72904 

25 6.024 .72985 

30 5.996 .73092 

35 5.957 .73242 

40 5.896 .73477 

45 5.78& .73892 

50 5.620 .74538 

55 5.380 .75462 

60 5.045 .76750 

65 4.599 .78465 

70 4.054 .80562 

71 11 5.799 .73850 

16 5.788 .73892 

21 5.773 .73950 

26 5.753 .74026 

31 5.725 .74135 

36 5.687 .74281 

41 5.626 .74515 

46 5.518 .74931 

51 5.352 .75569 

56 5.116 .76477 

61 4.787 .77742 

66 4.351 .7941!) 

71 3.822 .81454 

72 12 5.530 .74885 

17 5.520 .74923 

22.. 5.505 .74981 

27 5.485 .75058 

32 5.459 .75157 

37 5.422 .75300 

42 5.360 .75538 

47 5.251 .75958 

52 5.089 .7658Q 

57 4.858 .77469 



TWO. LIVES ANNUITIES SINGLE PREMIUMS. 



203 



Table XXV — {Continued). 

Ages. Single 

Older. \'oungei'. " Annuity. Premium. 

72 (\-2 4.534 .78716 

G7 4.110 .8034(5 

72 3.597 .82319 

73 13 5.266 .75900 

IS 5.255 .75943 

23 5.241 .75996 

lis : 5.222 .76069 

33 5.197 .76165 

38 5.161 .76304 

43... 5.098 .76546 

48 4.990 .76962 

53 4.832 .77569 

58 4.605 .78443 

63 4.288 .79661 

68 3.876 .81246 

73 3.380 .83154 

74 14 5.006 .76900 

19 4.996 .76939 

24 4.982 .76992 

■ 29 4.964 .7706:i 

34 4.940 .77154 

39 4.904 .77293 

44 4.841 .77534 

49 4.735 .77943 

54 4.580 .78538 

59 4.358 .79392 

64 4.048 .80584 

69 3.649 .82119 

74 3.170 .83962 

75 10 4.757 .77858 

15 4.751 .77881 

20 4.741 .77919 

25 4.728 .7796i> 

30 4.711 .78034- 

35 4.68S .7Sli>:; 

40 4.65.", .78257 



204 COMBINED OB ACTU ABIES ' EXPERIENCE TABLES. 



Table XXV — (Continued). 

Abes. Single 

Older. Younger. Annuity. Premium. 

75 45 4.588 .78507 

50 4.485 .78904 

55 4.333 .79488 

60 4.116 .80323 

65 3.815 .81481 

70 3.430 .82962 

75 2.967 .84742 

76 11 4.508 .78815 

16 4.501 .78842 

21 4.492 .78877 

26 4.480 .78923 

31 , 4.463 .78988 

36 4.441 .79073 

41., 4.406 .79208 

46 4.341 .79458 

.51 4.240 .79846 

56 '4.093 .80411 

61 3.881 .81227 

66 3.589 .82350 

71 3. 218 .83777 

76 2.773 .85488 

77 12 4.263 .79757 

17 4.257 .79781 

22 4.248 .79815 

27 4.236 .79862 

32 4.220 .79923 

37 4.199 .80003 

42 4.164 .80139 

47 4.100 .80385 

52 4.002 .80761 

57 3.859 .81311 

62 3.653 .82103 

67 3.371 .83188 

72 3.013 .84565 

77 2.58r, .86212 

78 13 4.024 .80677 



TWO LIVES ANNUITIES - 


— SINGLE PREMIUMS. 205 


Table XXV- 

Ages. 
Older Younger. 


- (Continued). 

Annuity. 


Single 
Premium. 


78 18 


4.018 


. 80700 


23 


4.010 


: 80731 


28 


3.998 


.80777 


33 


3.983 


.80834 


38 


3.963 


.80911 


43 


3.928 


.81046 


48 


3.865 


.812&9 


53 


3.770 


.81654 


58 


3.631 


.82188 


63 


3.431 


.82958 


68 


3.159 


. 8400;5 


73 


2.816 


.85323 


78 


2.405 


.86904 


79 14 


3.791 


.81573 


19 


3.785 


.81596 


24 


3.777 


.81627 


29 


3.766 


.81669 


34 


3.752 


.81723 


39 


3.733 


.81796 


44 


3.697 


.81935 


49 


3.636 


.8216!) 


54 


3 . 544 


.82523 


59 


3.410 


.8303S 


64 


3.216 


.83785 


69 


2.956 


.84785 


74 


2.626 


.86054 


79 


2.234 


.87562 


80 10 


3.567 


.82435 


15 


3.563 


.82450 


20 


3.558 


.82469 


25 


3.550 


.82500 


30 


3.540 


.82538 


35 


3.527 


.82588 


40 


~3 . 50& 


.82661 


45 


3.473 


.82796 


50. 


3.413 


.83026 



206 COMBINED OR ACTUARIES* EXPERIEKCE TABLES. 



Table XXV — (Continued). 

4.aES. Single 

Older. Yoimger. Annuity. Premium 

80 55 3.325 .83r.6(i 

60 :... 3.195 .8386(1 

65 3.009 .84580 

70 2.759 .8554:^ 

75 2.445 .86750 

80 2.069 .88196 

81 11 :; . :H5 . 83289 

16 3.;141 ' .83304 

21 3.336 .83323 

26 3.329 .83350 

31 3.320 .8338.-. 

36 3.307 .8343.-. 

41 3.289 .83503 

46 3.253 .83642 

51 3.196 .83862 

56 3.112 .84184 

61 2.987 .84665 

66 2.808 .85354 

71 2.570 .86269 

76 2.270 .87423 

81 1.913 .88796 

82 12 3.127 .84127 

17 3.124 .84139 

22 3.119 .84157 

27 3.112 .84184 

32 3.104 .84216 

37 3.092 .84261 

42 3.074 .84331 

47 3.039 .84465 

52 2.984 .84677 

57 2.904 .84985 

62 2.784 .85447 

67 2.614 .86100 

72 2.388 .86969 

77 2.103 .88065 

82 1.762 .89377 



TWO LIVES ANNUITIES SINGLE PREMIUMS. 207 



Table XXV — (Continued). 

/vw ^^"4- Single 

Oider. Younger. Annuity. Premium. 

S3 13 2.913 .84950 

18 2.910 .84962 

23 2.90B .84977 

28 2.899 .85003 

33 2.891 .85034 

38 2.881 .85073 

43 2.863 .85142 

48 2.829 .85273 

53 2.777 .85473 

5&...- 2.700 .85769 

63 2.586 .86208 

68 2.425 .86827 

73 2.211 .87650 

78 1.941 .88688 

83 1.618 .89931 

84 14 2.702 .85761 

19 2.699 .85773 

24 2.695 .85789 

29 2.689 .85811 

34 2.682 .85838 

39 2.672 .85877 

44 2.654 .85947 

49 2.622 .86069 

54 2.573 .86257 

59 2.500 .86538 

64 2.392 .86954 

69 2.240 .87538 

74 2.039 .88311 

79 1.785 .89280 

84 1.477 .90473 

^.5 15 2.492 .86569 

20 2.489 .86580 

25 2.485 .SGSOC) 

30 •. 2.480 .86615 

35 2.473 .86642 

40 2.464 .86677 



208 COMBINED OK ACTXJAKIES' EXPEEIENCB TABLES. 



Table XXV- 

Ages. 
Older. Younger. 


- (Continued). 

Annuity 


Premium. 


85 45 


2.447 


. 8()74M 


50 


2.416 


.80862 


55 


2.370 


.87038 


60 


2.302 


.87300 


65 


2.201 


.87688 


70 


2.059 


.88234 


75 


1.871 


.88958 


80 


1.633 


. 89873 


85 


1.339 


.91003 


80 16 


2.283 


.873T3 


21 


2.280 


.87385 


26 


2.277 


.87396 


31 


2.272 


.87415 


36 


2.266 


.87439 


41 


2.258 


.87469 


46 


2.241 


.87534 


51 


2.212 


.87646 


56 


2.170 


.87808 


61 


2.106 


.88054 


66 


2.012 


.88415 


71 


1.881 


.88919 


76 


1.707 


.89588 


81 


1.486 


.90439 


86 


1.205 


.91503 


87 17 


2.075 


.8817.1 


22 


2.073 


.88180 


27 


2.070 


.88192 


32 


2.065 


.88212 


37 


2.060 


.88231 


42 


2.052 


.88261 


47 


2.036 


. 88323 


52 


2.010 


. 88423 


57 


1.971 


.88573 


62 


1.912 


.88800 


67 


1.825 


.89135 


72 


1.705 


.89596 



TWO LIVES ANNUITIES SINGLE PREMIUMS. 209 



Older. 


Table XXV — 

ASHg. 

Younger. 


■ (Continued). 

Annuity. 


single 
Prenuum. 


87 


77 


1.545 


.90212 




82 


1.342 


.90992 




87 


1.072 


.92030 


88 


18 


1.868 


.88969 




23 


1.866 


.88977 




28 


1.863 


.88988 




33 


1.860 


.89000 




38 


1.855 


.89019 




43 


1.848 


.89040 




48 


1.832 


.89107 




53 


1.809 


.89196 




58 


1.774 


.89331 




63 


1.720 


.89538 




68 


1 . 641 


.89842 




73 


1.533 


.90257 




78... 


1.387 


.90819 




83 


1.202 


.91530 




88 


0.942 


.92530 


8d 


19 


1.664 


,89754 




24 


1.662 


.89761 




29 


1.659 


.89773 




34 


1.656 


.89785 




39 


1.652 


.89800 




44 


1 . 645 


.89827 




49 


1.631 


.89881 




54 


1.610 


.89962 




59 


1.579 


. 90080 




64 


1.530 


.90269 




69 


1.460 


.90538 




74 


1.363 


.90911 




79 


1.232 


.91415 




84 


r. 064 


.92062 




89 


0.815 


.93019 


90 


20 


1.463 


.90526 




25 


1.461 


.90534 




30 


1.459 


.90542 




14 







210 COMBINED OE ACTUARIES' EXPERIENCE TABLES. 



Older. 


Table XXV — 

Ages. 

Younger. 


(Conclvded). 

Annixity. 


Single 
Prenuumc 


90 


35 


1.456 


.90554 




40 


1.453 


.90565 




45 


1 . 446 


,90592 




50 


1.434 


.90639 




55 


1.415 


.90712 




60 


1.388 


.90815 




65 


1.345 


.90981 




70 


1.283 


.91219 




75 


1.197 


.91550 




80 


1.082 


.91992 




85 


0.930 


.92577 




90 


0.692 


.93492 



SINGLE LIFE COMMUTATION COLUMNS. 211 



Table XXVI — Single Life — Commutation 
Columns. 

COMBINED EXPERIENCE Table of Mortality, with 
Interest at 5^ Per Annum. 



Age. 


D. 




N.. 


M 


X. 


10.. 


61391, 


.325 


1077778.215 


10068, 


.5529 


11.. 


58072, 


.686 


1016386.890 


, 9673. 


3097 


12. . 


54932, 


.011 


958314.204 


9298, 


.0013 


13.. 


51959 


.825 


903382.193 


8941 


.6254 


14. . 


49146 


.647 


851422.368 


8602 


.7248 


15.. 


46483 , 


.568 


802275.721 


8279, 


.9623 


16.. 


43962, 


.672 


755792.153 


7972, 


.5695 


17.. 


41576, 


.020 


711829.481 


7679, 


.3781 


18.. 


39316, 


.564 


670253.461 


7399, 


.7327 


19.. 


37177, 


.227 


630936.897 


7132, 


.6123 


20.. 


35151, 


.728 


593759.670 


6877, 


.4581 


21. . 


33233, 


.755 


558607.942 


6633, 


.3773 


22. . 


31417, 


.712 


525374.187 


6399, 


.8938 


23. . 


29698 


.288 


493956.475 


6176 


.5519 


24. . 


28070 


.138 


464258.187 


5962, 


.6050 


25. 


26528, 


.524 


436188.049 


5757, 


.6649 


26.. 


25068, 


.955 


409659.525 


5561 


.3589 


27.. 


23686, 


.898 


384590.570 


5373, 


.0615 


28.. 


22378, 


.345 


360903.672 


5192, 


.4552 


29.. 


21139, 


.245 


338525.327 


5018. 


.9915 


30. . 


19966 


.023 


317386.082 


4852, 


.3997 


31.. 


18855, 


.058 


297420.059 


,4692, 


.1984 


32.. 


17803, 


.157 


278565.001 


4538 


.1566 


33.. 


16807, 


.082 


260761.844 


4389, 


.8512 


34. . 


15863. 


,979 


243954.762 


4247. 


.0851 


35.. 


14971. 


,133 


228090.783 


4109. 


.6671 


36. . 


14125. 


,793 


213119.650 


3977. 


,2389 


37.. 


13325. 


,535 


198993.857 


3849. 


.6369 


38.. 


12568. 


050 


185668.322 


3726. 


.7017 


39.. 


11850. 


999 


173100.272 


3608. 


,1291 


40.. 


11172. 


319 


161249.273 


3493. 


,7823 


41.. 


10530. 


049 


150076.954 


3383. 


,5278 



212 COMBINED OB ACTXJ ABIES ' EXPEEIENCE TABLES. 





Table '. 


y^y^Yi— {Conm 


med). 


Age. 


D.. 


N.. 


M,. 


42. 


9922.197 


139546.905 


3277.1063 


43.. 


9346.762 


129624.708 


3174.1573 


44. . 


8801.528 


120277.946 


3074.0071 


45. . 


8284.356 


111476.418 


2975.9549 


46.. 


7793.511 


103192.062 


2879.6039 


47.. 


7327.096 


95398.551 


2784.3078 


48.. 


6883.871 


88071.455 


2689.9924 


49.. 


6462.581 


81187.584 


2596.5056 


50. . 


6062.142 


74725 . 003 


2503.8080 


51. . 


5681.447 


68662.861 


2411.7873 


52.. 


5319.467 


62981.414 


2320.3519 


53. 


4975.236 


57661.947 


2229.4288 


54.. 


4647.852 


52686.711 


, 2138.9612 


55.. 


4336.608 


48038.859 


2049.0437 


56. . 


4040.628 


43702.251 


1959.5687 


57.. 


3759.223 


39661.623 


1870.5739 


58.. 


3491.854 


35902.400 


1782.2166 


59. . 


3237.828. 


32410.546 


1694.4692 


60.. 


2996.544 


29172.718 


1607.3669 


61.. 


2767.277 


26176.174 


1520.7923 


62.. 


2549.554 


23408.897 


1434.8441 


63. 


2342.869 


20859.343 


1349.5665 


64. . 


2146.871 


18516.474 


1265.1345 


65. . 


1961.166 


16369.603 


1181.6610 


66.. 


1785.442 


14408.437 


1099.3260 


67.. 


1619.458 


12622.995 


1018.3626 


68. . 


1462.950 


11003.537 


938.9718 


69. 


1315.777 


9540.587 


861.4635 


70.. 


1177.825 


8224.810 


786.1671 


71.. 


1048.900 


7046.985 


713.3294 


72.. 


928.868 


5998.085 


643.2447 


73.. 


817.576 


5069.217 


576.1851 


74. 


714.886 


4251 . 641 


512.4269 


75.. 


620.611 


3536.755 


452.1941 


76.. 


534.577 


2916.144 


395.7125 


77.. 


456.590 


2381.567 


343.1818 





SINGLE LIFE — ( 


:30MMUTATI0N COLUMNS. Zld 




Table XXVI— (Concluded). 


Age. 


D,. 


N.. 


M:,. 


78.. 


386.375 


1924.977 


294.7097 


79.. 


323.656 


1538.602 


250.3890 


80.. 


268.152 


1214.946 


210.2974 


81.. 


219.526 


946.794 


174.4400 


82.. 


177.411 


727.268 


142.7791 


83.. 


141.389 


549.857 


115.2054 


84. . 


110.969 


408.468 


91.5177 


S5. . 


85.6383 


297.4993 


71.4716 


s6. . 


64.8327 


211.8610 


54.7440 


S7.. 


48.0083 


147.0283 


41.0069 


s8. . 


34.6467 


99.0200 


29.93146 


89. . 


24.2437 


64.3733 


21.17825 


itO. . 


16.3383 


40.1296 


14.42738 


9J. 


10.5230 


23.7913 


9.39004 


92. . 


6.40412 


13.26836 


5.77228 


93. . 


3.62739 


6.86424 


3.30052 


94.. 


1.87510 


3.23685 


1.720962 


95.. 


.863787 


1.361751 


.798942 


96. . 


.342002 


.497964 


.318290 


97.. 


. 114441 


.155962 


.107014 


98.. 


.033536 


.041521 


.031558 


',•9. . 


.007985 


.007985 


.0076045 



'2U COMBINED OK ACTUABIES' EXPEEIENCE TABLES. 



Table XXVII — Single Life. 

ANNUITIES AND SINGLE PREMIUMS PER $1. 

COMBINED EXPERIENCE Table of Mortality, with 
Interest at 5^ Per Annum. 

single 

Aee. Annuity. Premium.. 

10 16.5559 .16400U 

11 16.5020 .166572 

12 16 . 4455 . 169264 

13 16.3862 .172087 

14 16.3241 .175042 

15 16 . 2593 . 178127 

16 16.1917 .181349 

17 16.1212 .184707 

18 16 . 0476 . 188209 

19 15.9711 .191854 

20 15.8913 .195651 

21 15.8085 .19959S 

22 15.7222 .203703 

23 15.6325 .207977 

24 15.5392 .212418 

25 15.4422 .2170':7 

26 15.3414 .221842 

27 15.2364 .226837 

28 15 . 1274 . 2320;!() 

29 15.0141 .237425 

30 14.8963 .243033 

31 14.7740 .248856 

32 14.6469 .254907 

33 14.5150 .261191 

34 14.3779 .267710 

35 14.2354 .274506 

36 14.0873 .281559 

37 18 . 9333 . 2^8892 

38 13.7730 .296522 

39 13.6064 .304458 

40 18.4329 .312718 



SINGLE LIFE ANNUITIES SINGLE PREMIUMS. 215 





Table XXVII— (Continued). 




Age. 


Annuity. 


single 
Premium. 


41 


13.2523 


.321321 


42 


13.0641 


.330280 


43 ... . 


12.8684 


..■',39600 


44 ... . 


12.6656 


.349258 


45 ... . 


12.4562 


.359226 


46 


12.2408 


.369487 


47..., 


12.0200 


.380002 


48 


11.7939 


.390767 


49.... 


11.5627 


.401775 


50... 


11.3265 


.413024 


51.... 


11.0855 


.424502 


52.... 


10.8398 


.436200 


53.... 


10.5898 


.448105 


54.... 


10.3357 


.460204 


55.... 


10.0775 


.472499 


56.... 


9.8157 


.484966 


57.... 


9.5505 


.497596 


58.... 


9.2818 


.510393 


59.... 


9 . 0100 


.523335 


60 


8.7355 


. 536407 


61 


8.4592 


.549563 


62 ... . 


8.1816 


.562782 


63.... 


7.9033 


.576032 


64.... 


7.6249 


.589292 


65.... 


7.3469 


.602530 


66 


7.0700 


.615716 


67.... 


6.7946 


.628829 


68.... 


6.5215 


.641834 


69 


6.2509 


.654718 


70.... 


5.9831 


. 667473 


71 


5.7185 


. 680077 


72 


5.4574 


.692504 


73.... 


5 . 2003 


.704748 


74.... 


4.9473 


.716795 


75 ... . 


4.6988 


.728627 


76.... 


4.4550 


.740235 



216 COMBINED OB ACTU ABIES ' EXPBBIENCB TABlOa. 



Age. 


Table XXVII— {Concluded). 

Annuity. 


single 
Premium. 


77.... 


4.2160 


.751619 


78 ... . 


3.9821 


.762756 


79.... 


3.7538 


.773626 


80 


3.5308 


. 784247 


81 


3.3129 


.794621 


82.. . 


3.0993 


. 804793 


83.... 


2 . 8890 


.814812 


84..., 


2.6809 


.824714 


85.... 


2.4739 


.834575 


86.... 


2.2678 


. 844389 


87.... 


2.0626 


.854163 


88.... 


1.8580 


.863905 


89.... 


1.6553 


.873557 


90 


1.4562 


.883040 


91 


1.2609 


.892335 


92 


1.0718 


.901339 


93.... 


.8923 


.909888 


94 


.7262 


.917797 


95 


.5765 


.924929 


96.... 


.4560 


.930667 


97 


.3628 


.935102 


98 


.2381 


.941019 



TWO LIVES ANNUITIES SINGLE PBEMIUMS. 217 



Table XXVIII — Two Lives. 

COMBINED EXPERIENCE Table of Mortality, with 
Interest at 5^ Per Annum. 

Ages. Single 

Older. Younger. Annuity. Premium. 

10 10 14.602 .25701 

11 11 14.542 .25990 

12 12 '. 14.478 .26295 

13 13 14.411 .26614 

14 14 14.341 .26947 

15 10 14.426 .26i'.42 

15 14.268 .27295 

16 11 14.357 .26872 

16 14.192 .27657 

17 12 14.285 .27214 

17 • 14.112 .28038 

18 13 14.210 .27571 

18 14.029 .28433 

19 14 14.131 .27947 

19 13.943 .28843 

20 10 14.190 .27667 

15 14.049 .28338 

20 13.853 .29272 

21 11 14.111 .28043 

16 13.964 .28743 

21 ' 13.760 .29714 

22 12 14.029 .28433 

17 13.875 .29166 

22 13.664 .30171 

23 13 13.943 .28843 

18 13.783 .29605 

23 • 13.564 .30648 

24 14 13.853 .29272 

19...' 13.687 .30062 

24 13.460 .31143 

25 . 10 13.881 .29138 

15 13.760 .29714 



218 COMBINED OR ACTUARIES' EXPERIENCE TABLES. 



Older. 


Table XXVIII- 

Aqbs. 

Younger. 


- (Continued). 

Annuity. 


Single 
Freminm. 


25 


20 


13.587 


.30538 




25 


13.352 


.31657 


26 


11 


13.789 


.29576 




16 ;.... 


13.663 


.30176 




21 


13.484 


.31029 




26. 


13 . 240 


.32190 


27 


12 


13.693 


.30034 




17 


13.562 


.30657 




22 


13.377 


.31538 




27 


13.124 


. 32743 


28 


13 


13.593 


.30510 




18 


13.457 


.31157 




23.. 


13.266 


.32066 




28 


13.003 


.33319 


29 


14 


13.489 


. 31005 




19 


13.348 


.31676 




24 


13.151 


.32614 




29 


12.878 


.33914 


30 


10 


13.484 


.31029 




15 


13.381 


.31519 




20 


13.235 


.32214 




25 


13.031 


.33185 




30 


. ■ 12.749 


.34528 


31 


11 


13.376 


.31542 




16 


13.269 


.32052 




21 


13.118 


.32772 




26 


12 ..907 


.33777 




31 


12.615 


.35166 


32 


12 


13.263 


.32081 




17 


13.152 


.32609 




22 


12.996 


.33352 




27 


12.7.78 


.34391 




32 


12.476 


.35828 


33 


13 


13.145 


.32643 




18 


13.031 


.33185 




23 


12.870 


.33952 



TWO LIVES ANNUITIES — 


-SINGLE PKEMIUMS. 219 


Table XXVIII- 

Ages. 
Older. Younger. 


— {Continued). 

Annuity. 


Single 
Prenuum. 


33 28 


12.645 


. 35024 


33 


12.332 


.36514 


34 14 


13.023 


.33224 


19 


12.905 


.33786 


24 


12.739 


.34576 


29 


12.507 
12.183 


.35681 


34 


.37224 


35 10 


12.978 


.33438 


15 


12.896 


. 33828 


20 


12.774 


.34410 


25 


12.603 
12.363 


.35224 


30 


.36367 


35 


12.028 


.37962 


36 11 


12 . 848 


.34057 


16 


12.763 


.34462 


21 


12.638 


.35057 


26 


12.462 


.35895 


31 


12.214 


.37076 


36 


11.867 


.38729 


37 12 


12.713 


.34700 


'17 


12.625 
12.497 


.35119 


22 


.35729 


27 


12.315 


.36595 


32 


12.060 


.37810 


37 


11.700 


.39524 


38 13 


12.572 


.35371 


18 


12.481 


. 35805 


23 


12.350 


.36429 


28 


12.163 


.37319 


33 


11.900 


.38571 


38 


11.526 


.40352 


39 14 


12.425 


.36071 


19 


12.331 


.36519 


24 


12.197 


.37157 


29 


12.005 


.38071 


34 


11.734 


.39362 



220 COMBINED OB ACTTJAEIES' EXPERIENCE TABLES. 



Table XXVlll — {C ontiniied) . 

Aqes. Single 

Older. Younger, Annuity. Premiuni 

39 39 11.346 .41209 

40 10 12.341 .36471 

15 12.271 .36805 

20 12.175 .37262 

25 12.038 .37914 

30 11.841 .38852 

35 11.561 .40185 

40 11.15S .42105 

41 11 12.183 .37224 

16 12.111 .37566 

21 12.012 .38038 

26 11.872 .38704 

31 11.670 .39667 

36 11.381 .41043 

41 10.963 .43034 

42 12 12.01S .38010 

17.... 11.944 .38362 

22 11.843 .38843 

27 . 11.699 .39528 

32 11.492 .40514 

37 11.194 .4]9n.", 

42 10.759 .4:oon 

43 13 11.845 .38833 

18 11.770 .30190 

23 11.667 .39681 

28 11.519 .40386 

33 11.307 .41396 

38 10.999 .42862 

48 10.547 .45015 

44 14 11.665 .39690 

19 11.589 .40052 

24 11.484 .40552 

29 11.333 .41272 

34 11.116 .42304 

39 10.797 .43824 

44 10.328 .46057 



TWO LIVES ANNUITIES — 


- SINGLE PREMIUMS. 221 




Table XXVni- 


— (Continued). 




Older. 


Aqes. 

Younger. 


Annuity. 


Single 
Prenuum. 


45 


10 


11.53::! 


. 10310 




15 


11.479 


.40576 




20 


11.402 


.40942 




25 


11.295 


4145:3 




30 


11.141 


.42185 




35 


10.918 


-i;324.S 




40 


10.588 


.44819 




45 


10.103 


47129 


46 


11 


11.343 


.41224 




16 


11.287 


.41491 




21 


11.209 


.41862 




26 


11.100 


.42381 




31 


10 . 943 


.43129 




36 


10.714 


.44219 




41 


10.373 


.45843 




46 


9.872 


.48228 


47 


12 


11.147 


.42157 




17 


11.090 


.42429 




22 


11.011 


.42805 




27 


10.900 


.43333 




32 


10.740 


. 44095 




37 


10.505 


.45214 




42 


10.152 


.46895 




47 


9.637 


.49348 


48 


13 


10.946 


.43114 




18 


10.888 


.43391 




23 


10.808 


.43772 




28 


10.695 


.44309 




33 


10.532 


.45085 




38 


10.291 


.46233 




43 


9.925 


.47976 




48 


9.399 


.50481 


49 


14 


10.740 


.44095 




19 


10.681 


.44376 




24 


10.600 


.44762 




29 


10.486 


.45304 



222 COMBINED OE ACTUARIES ' EXPERIENCE TABLES. 



Older. 

49 



50 



51 



52 



53 



Table XXVIII— (Continued). 

Agks. Single 

Younger. Annuity. Prenuum 

34 10.319 .46100 

39 10.072 .47276 

44 9.692 .49085 

49 9.156 .51638 

10 10.570 .44905 

15. 10.529 .45100 

20 10.469 .45386 

25 10.388 .45772 

30 10.272 .46323 

35 10.102 .47133 

40 9.847 .48348 

45 9.454 .50219 

50 8.910 .52810 

11 10.355 .45928 

16 10.313 .46129 

21 10.253 .46415 

26 10.171 .46805 

31 10.053 .47367 

36 9.880 .48190 

41 9.617 .49443 

46 9.212 .51371 

51 8.661 .53995 

12 10.135 .46976 

17 10.092 .47180 

22 10.032 .47466 

27 9.950 .47857 

32 9.830 .48429 

37 9.653 .49272 

42 9.381 .50566 

47 8.966 .52542 

52 8.409 .55195 

13 9.911 .4804.3 

18 9.867 .48253 

23 9.807 .48538 

28 9.724 .48933 

33 9.603 .49510 



TWO LIVES ANNUITIES SINGLE PREMIUMS. ^'I'.j 




Table XXVlll — {C ontinued) . 






Ages. 


Single 


Older. 


Younger. Annuity. 


Premium. 


53 


38 9.422 


.50371 




43 9 . 140 


.51714 




48 8.718 


.53724 




53 8.156 


.56400 


54 


14 9.682 


.49133 




19 ; 9.638 


. 49343 




24 9.578 


.49629 




29 9.494 


.50029 




34 9.372 


.50609 




39 9.187 


.51491 




44 8.895 


.528-81 




49 8.467 


.54919 




54 7.900 


.57619 


55 


10 9.479 


.50100 




15 9.449 


. 50243 




20 9.405 


.50452 




25 9.345 


.50738 




30 9.260 


.51143 




35 9.137 


.51729 




40 8.947 


. 52J634 




45 8.646 


.54066 




50 8.214 


.56124 




55 7.642 


.58847 


56 


11 9.243 


.51224 




16 9.212 


.51371 




21 9.168 


.51581 




26 9.108 


.51867 




31 9.023 


.52272 




36 8.899 


.52862 




41 8.703 


. 53796 




46 &.394 


.55267 




51 7 . 958 


.57343 




56 7.384 


. 60076 


57 


12 ► 9.003 


.52367 




17 8.971 


.52519 




22 8.928 


.52724 



224 COMBINED OR ACTUAEIES' EXPEBIENCE TABLES. 



Table XXVIII— {Continued). 

Ages. 

Older. Younger, Annuity. 

r>7 27 8.868 

32 8.783 

37 8.656 

42 8.455 

47 8 . 140 

52 7.701 

57 7.124 

58 13 8.759 

18 8.727 

23 8.683 

28 8.624 

83 8.539 

38 8.410 

43 8.203 

48 7.883 

53 7.442 

58 6.864 

59 14 8.511 

19 8.479 

24 8.436 

29 8.377 

34 8.292 

39 8.161 

44., 7.947 

49 7.624 

54 7.182 

59. 6.603 

60 10 8.282 

15 8.260 

20 8.229 

25 8.186 

30 8.127 

35. 8.041 

40 , 7 . 908' 

45 7.689 

50 7.364 



« 



Single 
Preiniuin. 

.53010 
.53415 
.54019 
.54976 
.56476 
.58566 
.61314 
.53528 
.53681 
.53891 
.54171 
.54576 
.55190 
.56176 
.57700 
.59800 
.62552 
.54709 
.54862 
.55066 
.55348 
.55752 
.56376 
.57396 
.58933 
.61038 
.63796 
.55800 
.55905 
.56052 
.56257 
.56538 
.56947 
.57581 
.58624 
. 60171 



TWO LIVES ANNUITIES - 


-SINGLE PREMIUMS. iiZD 


Older. 


T.1BLE XXVIII- 
Ages. 

Younger. 


— {Continued). 

Annuity. 


Single 
Premium. 


60 


55 


6.921 


.62281 




60 


6.342 


.65038 


61 


11 


8.029 


.57005 




16 


8.007 


.57110 




21 


7.976 


.57257 




26 


7.933 


.57462 




31 


7.875 


.57738 




36 


7.789 


.58147 




41 


7.653 » 


.58796 




46 


7.429 


.59862 




51 


7.103 


.61415 




56 


6.661 


.63519 




61 


6.083 


.66272 


62 


12 


7.774 


.58219 




17 


7.752 


.58323 




22 


■7.721 


.58471 




27 


7.679 


.58671 




32 


7.621 


.58947 




37 


7.535 


.59357 




42 


7.396 


.60019 




47 


7.168 


.61105 




52 


6 . 843 


.62653 




57 


6.401 


.64757 




62 


5.825 


.67500 


C3 


13 


7.518 


.59438 




18 


7.496 


.59542 




23 


7.465 


.59690 




28 


7.424 


.59886 




33 


7.367 


.60157 




38 


7.280 


.60571 




43 


7.137 


.61253 




48 


6.907 


.62348 




53 


6.582 


.63895 




58 


6.142 


.65990 




63 


5.569 


.68719 


64 


14 

15 


7.261 


.60662 



226 COMBINED OR ACTUAEIES' EXPERIENCE TABLES. 



Table XXVIII - 

Ages. 
Older. Younger. 


— (Continued). 

Annuity. 


single 
Premiuffi. 


64 19 


7.239 


.60767 


24 


7,209 


.60909 


29 


7.168 


.61105 


34 


7.112 


.61371 


39 


7.025 


.61786 


44 


6.877 


.62491 


49 


6.647 


.63586 


54 


6.323 


.65129 


39 


5.884 


.67219 


64 


5.316 


.69923 


65 10 


7.019 


.61814 


15 


7.004 


.61886 


20 


6.982 


.61990 


25 


6.953 


.62129 


30 


6.913 


.62319 


35 


6.857 


.62586 


40 


6.768 


.63010 


45 


6.618 


.63724 


50 


6.388 


.64819 


55 


6.065 


.66357 


60 


5.628 


. 68438 


65 


5.068 


.71105 


66 11 


6.762 


.63038 


16 


6.747 


.63110 


21 


6.726 


.63209 


26 


6.697 


. 63348. 


31 


6.658 


. 63533 


36 


6.602 


.63800 


41 


6.512 


.64228 


46 


6.359 


.64957 


51 


6.130 


.66048 


56 


5 . 810 


. 67571 


61 


5.376 


.69638 


66 


4.823 


.72272 


67 12 


6.506 


.64257 


17 


6.491 


.64328 



TWO LIVES ANNUITIES — 


- SINGLE PREMIUMS. 2z7 


Older. 


Table XXVIII- 

Agbs. 

Younger. 


- (Continued). 

Annuity. 


Single 
Prenuum. 


67 


22 


6.470 


.64429 




27. ...T 


6.442 


.64561. 




32 


6.404 


. 64743 




37 


6 . 348 


. 65010 




42 


6.257 


. 65443 




47 


6.102 


.66180 




52 


5.874 


.67267 




57 


5.557 


.68777 




62 


5.126 


.70828 




67 


4.583 


.73415 


68 


13 


6.251 


.65471 




18 


6.236 


.65542 




23 


6.216 


.65638 




28 


6.189 


.65767 




33 


6.151 


.65947 




38 


6.096 


.66209 




43 


6.003 


.66653 




48 


5.847 


.67396 




53 


5.622 


.68466 




58 


5.307 


.69967 




63 


4.881 


.71995 




68 


4.349 


. 74528 


69 


14 


5.999 


. 66671 




19 


5.984 


. 66743 




24 


5.964 


.66838 




29 


5.937 


.66967 




34 


5.901 


.671?8 




39 


5.846 


. 6740O 




44 


5.750 


.67857 




49 


5.595 


. 68595 




54 


5.372 


.69657 




59 


5.060 


.71143 




64 


4.641 


.73138 




69 


4.120 


.75619 


70 


10 


5.757 


.67824 




15 


5.748 


.67867 



228 COMBINED OR ACTUAKIES' EXPEEIENCB TABLES. 



Table XXVIII 

Ages. 
Older. Younger. 

70 20 

25 

30 

35 

40 

45 

50 

55 

60 

65 

70 

71 11 

16 

21 

26 

31 

36 

41 

46 

51 

56 

61 

66 

71 

72 12 

17 

22 

27 

32 

37 

42 

47 

52 

57 

62 

67 



(Continued). 



5. 
5. 
5. 
5. 

5. 
5. 
5. 
4. 
4. 



Annuity. 

5.733 
714 
.688 
.652 
.597 
,500 
.346 
,126 
.817 
.405 
3.897 
5.509 
5.499 
5.485 
5.466 
5.441 
5.407 
5. 351 
5.252 
5.100 
4.883 
4.579 
4.175 
3.680 
5.263 
5.254 
5.240 
5.222 
5.198 
5.164 
5.108 
5.008 
4.858 
4.645 
4.345 
3.950 



Single 
Premium 

.67938 

.68029 

.6815:^ 

.68323 

.68586 

. 6904,s 

.6978] 

.70828 

.72300 

.74262 

.76681 

.69005 

.69052 

.69119 

. 69209 

.69328 

.69491 

.69757 

.70228 

.70952 

.71986 

.73433 

.75357 

.77714 

.70176 

.70219 

.70286 

.70371 

.70486 

.70648 

.70914 

.71391 

.72105 

.73119 

.74547 

.76429 



TWO LIVES — ANNUITIES SINGLE PREMIUMS. 229 



Table XXVITI- 

Ages. 
Older. Younger. 


- {Continued). 

Annuity. 


Single 
Premium. 


~ii 72 


3.469 


.73719 


73 1-^ 


5.021 
5.011 


7132S 


18 


.71376 


23 


4.998 


.71438 


28 


4.981 


71519 


33 


4.957 


.71634 


38 


4.924 


.71791 


43 


4.867 


.72062 


48 


4.767 


.72538 


53 


4.621 


7323?, 


5& 


4.411 


.74233 


63 


4.116 


.'75638 


68 


3.731 


.77471 


73 


3.264 


.79695 


74 14 


4.782 


.72466 


19 


4.772 


.72514 


' 24 


4.760 


.72571 


29 


4.743 


.72653 


34 


4.720 


.72762 


39 


4.688 


.72914 


44 


4.629 


.73195 


49 


4.531 


.73662 


54 


4.387 


.74348 


59 


4.181 


.75328 


64 


3.892 


76704 


69 


3.518 


.78486 


74 '. 


3.066 


.80638 


75 10 


4.552 


.73561 


15 


4.646 


.73590 


20 


4.537 


.73634 


25 


4.525 


.73690 


30 


4.509 


.73767 


35 


4.487 


.73872 


40 


4.455 


. 74024 


45 


4.395 


.74309 


50 


4.299 


.74767 



230 COMBINED OK ACTU ABIES ' EXPERIENCE TABLES. 



Table XXVIII— (Continued). 

Ages. 

Older. Younger. Animity. 

75 55 4.158 

60 3.956 

65 3 . 674 

70 3.311 

75 2.874 

76 11 4.321 

16 4.315 

21 4.306 

26 4.295 

31 4.279 

36 4.258 

41 4.226 

46 4.166 

51 4.072 

56 3.934 

61 3.736 

66 3.462 

71 3.111 

76 2.689 

77 12 4.093 

17 4.087 

22 4.079 

27 4.068 

32 4.053 

37 4.034 

42 4.001 

47 3.941 

52 3.849 

57 3.716 

62 3.522 

67 3.256 

72 2.91.'' 

77 2.511 

78 13 3.870 

18 3.865 

23 3.857 



Single 
Premium. 

.75438' 
.76400 
.77743 
.79471 
.81552 
.74662 
.74690 
.74733 
.74786 
.74862 
.74962 
.75114 
.75400 
.75847 
.76505 
. 77447 
.78752 
.80424 
.82433 
. 75748 
.75777 
.75814 
.75867 
.75938 
.76029 
.76185 
.76471 
.76909 
.77542 
.78466 
.797.S;i 
.81343 
.83281 
.76810 
.76833 
.76872 



TWO LIVES ANNUITIES • 



•SINGLE PREMIUMS. 



231 



Table XXVIII — 

Aqeb. 
Older. Younger. 


■ (Continued). 

Annuity. 


Single 
Premium. 


78 28 


3.846 


.76923 


33 


3.832 


.76990 


38 


3.813 


.77081 


43 


3.780 


.77238 


48 


3.721 


.77519 


53 


3.632 


.77942 


5& 


3.502 


.78561 


63 


3.313 


.79462 


68 


3.056 


.80685 


73 


2.731 


.82233 


78 


2.339 


.84100 


79 14 


3.652 


. 77847 


19 


3 . 647 


.77872 


24 


3.639 


.77909 


29 


3 . 629 


.77957 


34 


3.616 


.78019 


39 


3.598 


.78105 


44 


3.564 


.78267 


49 


3.506 
3.420 


. 78542 


54 


.78952 


59 


3.294 


.79552 


64 


3.111 


.80424 


6a 


2.863 


.81605 


74 


2.550 


.83095 


79 


2.175 


.84881 


80 10 


3.442 


.78847 


15 


3.439 
3.433 


.78862 


20 


.78891 


25 


3.426 


.78923 


30 


3.417 


.78967 


35 


3.404 


.79029 


40 


3.387 


.79110 


45 


3.353 
3.297 
3.213 
3.091 


.79272 


50 


.79538 


55 


.79938 


60 


.80519 



232 COMBINED OE ACTUARIES' EXPEEIENCE TABLES. 



Table XXVIII— (( 


Continued) . 




Ages. 




Single 


Older. Younger. 


Annuity. 


Premium 


80 65 


2.914 


.81363 


70 


2.677 


.82491 


75 


2.377 


.83919 


80 


2.017 


.85634 


81 11 


3.233 


.79843 


16 


3.230 


.79857 


21 


3.225 


.79881 


26 


3.218 


.79914 


31 


3.209 


.79957 


36 


3.197 


.80015 


41 


3.180 


.80095 


46 


3.146 


.80257 


51 


3.092 


.80514 


56 


3.012 


.80895 


61 


2.894 


.81457 


66 


2.724 


.82267 


71 


2.497 


.83348 


76 


2.210 


.84714 


81 


1.867 


.86348 


82 12 


3.028 


.80819 


17 


3.025 


.80833 


22 


3.020 


.80857 


27 


3.013 


.80891 


32 


3.005 


.80928 


37 


2.994 


.80981 


42 


2.977 


.81062 


47 


2.944 


.81219 


52 


' 2.892 


.81466 


57 


2.815 


.81833 


62 


2.701 


.82376 


67 


2.539 


.83147 


.72 


2.323 


.84176 


77 


2.050 


.85476 


82 


1.722 


.87038 


83 13 


2.825 


.81786 


18 


2.822 


.81800 



TWO LIVES ANNUITIES — 


-SINGLE PREMIUMS. 'l.)-> 


Table XXVni- 

Agks. 
Older. Younger. 


— {Continued). 

Annuity. 


Single 
Premium. 


-83 23 


2.818 


.81819 


28 


2.812 


.81847 


33 


2.804 


.81886 


38 


2.794 


.81933 


43 


2.777 


.82015 


4& 


2.745 


.82166 


53 


2.695 


.82405 


58 


2.622 


.82752 


. 63 


2.513 


.83272 


68 


2.359 


.84005 


73 


2.154 


.84981 


78 


1.894 


.86219 


83 


1.582 


.87704 


84 14 


2.624 


.82743 


19 


2.621 


.82757 


24 


2.617 


.82777 


29 


2.612 


.82800 


34 


2.605 


.82833 


39 


2.595 


.82881 


44 


2.579 


.82957 


49 


2 . 548 


.83105 


54 


2.501 


.83328 


59 


2.432 


.83657 


64 


2.328 


.84152 


69 


2.182 


. 84847 


74 


1.989 


.85867 


79 


1.744 


. 86953 


84 


1.447 


.88348 


85 15 


2.424 


.83695 


20 


2.421 


.83709 


25 


2.418 


.83724 


30 


2.413 


.83748 


35 


2.406 


.83781 


40 


2.398 


.83819 


45 


2.381 


.83900 


50 


2.352 


.84038' 



234 COMBINED OB ACTUARIES' EXPERIENCE TABLES. 



Table XXVIII— ( 


Continued). 




Ages. 
Older. Younger. 


Annuity. 


Single 
Premium. 


85 65 


2.308 


.84248 


60 


2.242 


.84561 


65 


2.145 


.85024 


70 


2.008 


.85676 


75 


1.828 


. 8653a 


80 


1.598 


.87629 


85 


1.313 


.88986 


86 16 


2.225 


.84643 


21 


2.222 


.84657 


26 


2.219 


.84671 


31 


2.214 


.84695 


36 


2.208 


.84724 


41 


2.200 


.84762 


46 


2.184 


.84838 


51 


2.157 


.84967 


56 


2.116 


.85161 


61 


2.055 


.85452 


66 


1.964 


.85886 


71 


1.837 


.86491 


76 


1.669 


.87290 


81 


1.456 


.88304 


86 


1:182 


.89609 


87 17 


2.025 


.85595 


22 


2.023 


.85605 


27 


2.020 


.85619 


32 


2.016 


.85638 


37 


2.011 


.85662 


42 


2.003 


.85700 


47 


1.987 


. 85777 


52 


1.962 


.85895 


57 


1.925 


.86071 


62 


1.868 


.86343 


67 


1.784 


.86743 


72 


1.668 


.87295 


77 


1.513 


.88034 


82 


1.316 


.88971 



TWO LIVES ANNUITIES SINGLE PREMIUMS. 235 



Table XXVIII- 


- (Continued). 




Ages. 




Single 


Older. Younger. 


Annuity. 


Premium. 


87 87 


1.054 


. 902 1 i) 


88" 18 


1.826 


.86542 


23 


1.824 


.86552 


28 


1.822 


.86561 


33 


1.818 


.86581 


38 


1.813 


.86605 


43 


1.806 


.86638 


48 


1.791 


.86709 


53 


1.769 
1.735 


.86814 


58 


.86976 


63 


1.683 


.87224 


68 


1.607 


.87586 


73 


1.501 


.88090 


78 


1.360 


.88762 


83 


1.180 
0.927 


.&961& 


88 . . ; 


. 90824 


89 19-. 


1.629 


.87481 


24 


1.627 


.87491 


29 


1.625 


. 87500 


34 


1.621 


.87515 


39 


1.617 


.8753S 


44 


1.611 
1.597 


.87566 


49 


.87634 


54 


1.577 


.87729 


59 


1.546 


.87876 


64 


1.499 


. 88100 


69 


1.431 


.88424 


74 


1.337 


.88872 


79 


1.210 


. 89476 


84 


1 . 046 


.90257 


89 


0.802 


.91419 


90 20 


1.434 


.88410 


25 


1.433 


.88415 


30 


1.431 


.88424 


35 


1.428 


. 8843R 


40 


1.424 


.88457 



236 COMBINED OR ACTtTAKIES' EXPEKIENCE TABLES. 



Table XXVni— (Concluded). 

Ages. Single 

Older. Younger. Annuity. Premium 

90 45 1.41S .88480 

50 1.406 .88541' 

55 1.388 .88629 

60 1.361 .88757 

65 1.320 .88920 

70 1.259 .89243 

75 1.176 .89638 

80 1.063 .90176 

85 0.915 .90881 

90 0.682 .91990 



AMERICAN MORTALITY TABLE. 237 



Table XXIX. 
AMERICAN EXPERIENCE Table of Mortality. 

Age. Ix <*x tafion. 

10 100,000 749 48.72 

11...! 99,251 746 48.09 

12 98,505 743 47. 4& 

13 97,762 740 46.80 

14 " 97,022 737 46.16 

15 96,285 735 45.51 

16 95,550 732 44.85 

17 94,818 729 44.1'J 

18 94,089 727 43.53 

19 93,362 725 42.87 

20 92,637 723 42.20 

21 91,914 72^ 41.53 

22 91,192 721 40.85 

23 90,471 720 40.17 

24 89,751 719 39.49 

25 89,032 718 38.81 

26 88,314 718 38.12 

27 87,596 718 37.43 

28 86,878 718 36.73 

29 86,160 719 36.03 

30 85,441 720 35.33 

31 84,721 721 34.63 

32 84,000 723 33.92 

33 83,277 726 33.21 

34 82,551 729 32.50 

35 81,822 732 31.78 

36 81,090 737 31.07 

37 80,353 742 30 . 35 

88 79,611 749 29.63 

39 78,862 756 28.90 

40 78,106 765 28.18 

41 77,341 774 27.45 

42 76,567 785 26.72 



238 



AMERICAN EXPBEIESrCE TABLES. 



Table XXIX 

Age. 

43 

44 

45 

46 

47 

48 

49 

50 

51 

52 

53 . . 

54 '. . . 

:,r> 

:>G 

57 

58 

59 

GO 

01 

<)2 

<!3 

<;4 

(;5 

<i6 

(i7 

(18 

(ly 

70 

71 

72 

73 

74 

75 

76 

77 

78 



(Continued). 



75,782 
74,985 
74,173 
73,345 
72,497 
71,627 
70,731 
69,804 
68,842 
67,841 
66,797 
65,706 
64,563 
63,364 
62,104 
60,779 
59,385 
57,917 
56,371 
54,743 
53,030 
51,230 
49,341 
47,361 
45,291 
43,133 
40,890 
38,569 
36,178 
33,730 
31,243 
28,738 
26,237 
23,761 
21,330 
18,961 



dx 

797 

812 

828 

848 

870 

896 

927 

962 

1,001 

1,044 

1,091 

1,143 

1,199 

1,260 

1,325 

1,394 

1,468 

1,546 

1,628 

1,713 

1,800 

1,889 

1,980 

2,070 

2,15& 

2,243 

2,321 

2,391 

2,448 

2,487 

2,505 

2,501 

2,476 

2,431 

2,369 

2,291 



Expec- 
tation. 

25.99 

25.27 

24.54 

23.81 

23.08 

22.35 

21 . 63 

20.91 

20.20 

19.49 

18.79 

18.09 

17.40 

16.72 

16.05 

15.39 

14.74 

14.10 

13.47 

12.86. 

12.26 

11.67 

11.10 

10.54 

10.00 

9.47 

8.97 

8.48 

8.00 

7.55 

7.11 

6.68 

6.27 

5.88 

5.49 

5.11 



AMEKICAK MORTALITY TABLE. 239 

Table XXIX — (Concluded). 



Age. 

79. 
80. 
81. 
82. 
83. 
84. 
85. 
86. 
87. 
88. 
89. 
90. 
91. 
92. 
93. 
94. 
95. 



ix 


dx 


Expec- 
tation. 


16,670 


2,196 


4.75 


14,474 


2,091 


4.39 


12,383 


1,964 


4.05 


10,419 


1,816 


3.71 


8,603 


1,648 


3.39 


6,955 


1,470 


3.08 


5,485 


1,292 


2.77 


4,193 


1,114 


2.47 


3,079 


933 


2.18 


2,146 


744 


1.91 


1,402 


555 


1.66 


847 


385 


1.42 


462 


246 


1.19 


216 


137 


.98 


79 


58 


.80 


21 


18 


.64 


3 


3 


.50 



240 



AMEKICAN EXPERIENCE TABLES. 



Table XXX — Single Life — Commutation 
Columns. 

AMEEICAN EXPERIENCE Tahle of Mortality, with 
Interest at 5^ Per Annum. 



Age. l-'.T. 

10 61391.32500000 

11 58030.00421179 

12 54851.27005710 

13 51845.27581870 

14 49002.70264490 

15 46314.73147350 

16 43772.55573600 

17 41368.77955242 

18 39095.92243785 

19 36946.51397352 

20 34913.91075876 

21 32991.82807704 

22 31173.97334504 

23 29454.76108230 

24 27828.90409041 

25 26291.39621864 

26 24837.49382922 

27 23462.44143872 

28 22162.02525592 

29 20932.25493120 

30 19769.12070545 

31 18669.07465787 

32 17628.75828000 

33 16644.78551358 

34 15713.97909480 

35 14833.53329016 

36 14000.78937690 

37 13212.896177.39 

38 12467.50931496 

39 .11762.10721014 

40 11094.61988208 

41 10462.81422560 

42 9864.86318454 

43 9298.78484080 

44 8762.84683005 

45 8255.19603623 

46 7774.32576115 



1074639.54587172 
1013248.22087172 
955218.21665093 
900366.94660283 
848521.67078413 
799518.96813923 
753204.23666573 
709431.68092973 
668062.90137731 
628966.97893946 
592020.46496594 
557106.55420718 
524114.72613014 
492940.75278510 
463485.99170280 
435657.08671239 
409365.69049375 
384528.19666453 
361065.75522581 
338903.72996989 
317971.47503869 
298202.35433324 
279533.27967537 
261904.52139537 
245259.73588179 
229545.75678699 
214712.22349683 
200711.43411993 
187498.53794254 
175031.02862758 
163268.92141744 
152174.30153530 
141711.48730976 
131846.62412522 
122547 . 83928442 
113784.99245437 
105529.79641814 



10218.01327733 
9780.08848912 
9364.68777380 
8970.65901075 
8596.9087277.T 
8242.39912505 
7905.6871578.') 
7586.31798077 
7283 . 40342692 
6995.70483800 
6722.45996500 
6462.94463872 
6216.1290325a 
5981.39212528 
5758.14323008 
5545 . 8205384.'-) 
5343.88969431 
5151.57460055 
4968.41736703 
4793.98190927 
4627.62152272 
4468.96270432 
4317.6491957!)' 
4173.14134933 
4034.94376453 
3902.78315041 
3776.39792629 
3655.20880698 
3539.00768986 
3427.29586033 
3319.90932625 
3216.41890225 
3116.69703637 
3020.37408237 
2927.23560236 
2836.86283624 
2749.09759348 



SINGLE LIFE ■ 



COMMUTATION COLUMNS. 



241 



Table XXX • 

Age. Dx. 

47 7318.51487737 

48 6886.37091297 

49 6476.40691821 

50 6087.16916892 

61 5717.40864514 

62 5365.97548035 

53 5031.80865842 

54 4713.92716032 

55 4411.35736320 

56 4123.27036464 

67 3848.83702224 

58 3587.35344689 

69 3338.16743550 

60 3100.61671184 

61 2874.14364391 

82 2658.22701090 

63 2452.42538000 

64 2256.36438630 

65 2069.68126968 

66 1892.02600983 

67 1723.17308970 

68 1562.92209835 

69 1411.09263720 

70 1267.61531073 

71 1132.41155758 

72 1. 1005.51086340 

73 887 . 02095029 

74 777.04908104 

75 675.64210550 

76 582.74422764 

77 498.21270210 

78 421.78953071 

79 353.16761940 

80 292.04146378 

81 237.95383311 

82 190.67926509 

83 149.94710689 

84 115.45056575 

85 86.71340715 

86 63.13135941 

87 44.15101260 

88 29. 30699922 

89 18.23477652 

16 



■ (Continued). 

97755.47065699 

90436.95577962 

83550.58486065 

77074.17704844 

70987.00877952 

65269.60013438 

59903.62465403 

54871.81599561 

50157.88883529 

45746.53147209 

41623.26110745 

37774.42408521 

34187.07063832 

30848.90320282 

27748.28649098 

24874.14284707 

22215.91583017 

19763.49045017 

17507.12606387 

15437.44479419 

13545.41878436 

11822.24569466 

10259.32359631 

8848.23095911 

7580.61564838 

6448,20409080 

5442.69322740 

4555.67227711 

3778.62319607 

3102.98109057 

2520.23686293 

2022.02416083 

1600.23463012 

1247.06701072 

955 . 02554694 

717.07171383 

526.39244874 

376.44534185 

260.99477610 

174.28136895 

111.15000954 

66.99899694 

37.69199772 



2663.49266340 

2579.84902770 

2497.8077(1434 

2416.96990663 

2337.07468109 

2257.89923474 

2179.25486090 

2100.983553.38 

2022.88647818 

1944.86423894 

1866.77692334 

1788.57156759 

1710.2116213!! 

1631.62147803 

1552.79679737 

1473.74388497 

1394.52448697 

1315.24562897 

1236.00872825 

1156.9096488") 

1078.1529798r> 

999.9579577.") 

922.55319411 

846.270813,-)! 

771.42985953 

698.4535596:) 

627.84506808 

560.1121726S 

495. 707 67 11'^ 

434.98317(191 

378.20141047 

325.50274488 

276.96603126 

232.65740514 

192.47639367 

156.5.i.301363 

124 . 88080555 

97.524582S5 

74.28507305 

54.83224301 

38,85815141 

26.11657160 

16.43991416 



242 



AMERICAN EXPEEIENCK TABLES. 





Table XXX - 


- {Concluded). 




Age. 


D.. 


N.. 


M^. 


90 


10.49171277 


19.45722120 


9.56517911 


91 


5.45024172 


8.96550843 


5.02331101 


H2 


2.42682264 


3.51526671 


2.25942967 


93... 


.84532212 


1.08844407 


.79349131 


94 


.21400554 


.24312195 


.20242839 


95 


.02911641 


.02911641 


.02772993 



SINGLE LIFE ANNUITIES SINGLE PREMIUMS. 243 



Table XXXI — Single Life. 

ANNUITIES AND SINGLE PREMIUMS PER $1. 

AMEEICAN EXPERIENCE Table of Mortality, with 
Interest at 5^ Per Annum. 

Single 

Age. Annuity. Premium. 

10 16.50475 .1664407 

11 16.46076 .1685351 

12 16.41469 .1707287 

13 16.36642 .1730276 

14 16 . 31581 . 1754375 

15 16.26274 .1779650 

10 16 . 20722 . 1806083 

17 16 . 14896 . 1833827 

IS 16 . 08779 . 1862957 

19 16 . 02372 . 1893469 

20 15 . 95658 . 1925439 

21 15.88620 .1958953 

22 ; 15 . 81257 . 1994013 

23 15 . 7S552 . 2030705 

24 15 . 65484 . 2069124 

25 15.57033 .2109368 

26 15.48176 .2151541 

27 15.38910 .2195669 

28 15 . 29210 . 2241862 

29 15.19051 .2290238 

30 15 . 08425 . 2340834 

31 14.97307 .2393780 

32 14.85666 .2449208 

33 14.73492 .2507176 

34, 14.60774 .2567742 

35 14.47479 .2631055 

36 14.33572 .2697275 

37 14.19057 .2766394 

38 14.03897 .2838584 

39 13.88092 .2913845 

40 13 . 71604 . 2992359 



244 



AMERICAN EXPERIENCE TABLES. 



Table XXXI — (Continued). 

Age. Annuity. 


single 
Premium. 


41 


13.54430 


.3074145 


42 


13.36528 


.3159393 


43 


13.17891 


.3248138 


44 


12.98494 


.3340503 


45 


12.78344 


.3436458 


46 


12.57414 


.3536124 


47' 


12.35728 


.3639390 


48 


12.13275 


.3746311 


49 


11.90076 


.3856781 


50 


11.66175 


.3970598 


51 


11.41594 


.4087648 


52 


11.16361 


.4207810 


53 


10.90499 


.4330958 


54 


10.64036 


.4456972 


55 


10 37017 


.4585633 


5(! 


10.09472 


.4716801 


57 


9.81450 


.4850235 


5S 


9.52988 


.4985768 


59 


9.24127 


.5123205 


CO 


8.94928 


.5262248 


(il 


8.65445 


.5402642 


62 


8.35742 


.5544086 


03 


8.05876 


.5686310 


64 


7.75900 


.5829048 


65 


7.45885 


.5971978 


66 


7.15921 


,6114659 


67 


6.86074 


.6256789 


68 


6.56420 


.6398004 


69 


6.27048 


.6537863 


70 


5.98022 


.6676088 


71 


5.69422 


.6812272 


72 


5.41286 


.6946255 


73 


5.13592 


.7078131 


74 


4.86279 


.7208198 


75 


4.59264 


.7336839 


76 


4.32477 


.7464392 



SINGLE LIFE ANNUITIES ■ 


— SINGLE PREMl 


[UMS. Z40 


Table XXXI- 

Age. 


- (Concluded). 

Annuity. 


Single 
Premium. 


t i 


4.05856 
3.79392 


.7591162 


78 


.7717182 


79 


3.53109 


.7842337 


80 


3.27017 


.7966584 


81 


3.01349 


.8088814 


82 


2.76062 


.8209229 


fi3 


2.51052 


.8328324 


^4 


2.26066 


.8447301 


85 


2.00986 


.8566738 


.SG 


1.76061 


.8685428 


87 


1.51750 


.8801201 


88 


1.28611 


.8911386 


S9 


1.06704 


.9015688 


!)0 


0.85453 


.9116885 


91 


. 64497 


.9216672 


<) • 


0.44851 
0.28761 
0.13605 


.9310234 


i)3 


.9386849 


!M 


.9459024 



246 



AMERICAN EXPEBIENCE TABLES. 



Table XXXII 



Two Lives — Commutation 
Columns. 



AMERICAN EXPERIENCE Table of Moitaliti/, with 
Interest at 5^/ Per Annum (Makehamized) . 



Equal 



M, 



Ages. 


'-'XX. 


'^xx. 


"•■xx. 


10 


0149081923 


95044723404 


1023143208 


11 


5766966183 


88895041541 


15338408.50 


12 


5408391362 


83128075358 


1449883457 


13 


5072023946 


77720283900 


13710.58510 


14 


4756496579 


72048200050 


1297056110 


15 


4460442902 


07891703470 


1227492231 


16 


4182642793 


03431320508 


1162103724 


17 


3922008530 


59248077770 


110064288S 


18 


3677479822 


55320069240 


1042870550 


19 


3447996013 


51049189423 


988511307 


20 


3232714110 


48201192810 


93741922H 


21 


3030695553 


44968478700 


889339454 


22 


2841133832 


41937783146 


844090540 


23 


2663211370 


39096049314 


801400205 


24 


2496280800 


36433437944 


701355182 


25 


2339618910 


33937157144 


723503817 


26 


2192554707 


31597538234 


087910065 


27 


2054512207 


29404983528 


05427488S 


28 


1924949215 


27350471320 


022545790 


29 


1803355631 


25425522105 


5920in^SS 


30 


1689132981 


23622166474 


564207Hn'( 


31 


1581924052 


21933033494 


537493919 


32 


1481274079 


20351100442 


512173004 


33 


1386727080 


18869835363 


4881C34S7 


34 


1297959069 


17483108283 


465430098 


35 


1214540181 


16185149214 


443818824 


36 


1136192225 


14970009033 


423300095 


37 


1062594514 


13834410808 


403812705 


38 


993423802 


12771822294 


385241804 


39 


928383295 


11778398492 


367507141 


40 


867266582 


10850015198 


350599192 


41 


809790539 


9982748610 


334421558 


42 


755757090 


9172958078 


318949503 


43 


704903701 


8417200982 


304084602 


44 


C57082070 


7712297280 


289829832 


45 


012065025 


705.5215211 


276102380 


46 


569679391 


6443150186 


262862734 


47 


529780268 


5873470795 


2.50091198 





TWO LfVES 


COMMUTATION 


COLUMNS. 




Table XXXII — (Continued). 


Equal 
Ages. 


D„. 


N... 


M„., 


48 


492203910 


5343690527 


237742451 


49 


456788372 


4851486611 


225705211 


50 


423436938 


4394698239 


214165573 


51 


391998.599 


3971201300 


202890905 


52 


362360883 


3579262701 


191919800 


53 


334411123 


3216901818 


181225.307 


54 


308066815 


2882490695 


170805355 


55 


283224.591 


2574423879 


160632970 


56 


259809304 


2291199289 


150704580 


57 


237730714 


2031389984 


141003850 


58 


210939407 


17930.53270 


131527361 


59 


197356776 


1576713863 


122275161 


60 


178927879 


1379357087 


113244218 


61 


161610480 


1200429208 


104447193 


62 


145349245 


1038818728 


95881680 


63 


130120795 


893469483 


8757462:j 


64 


11.5882543 


763348689 . 


79532597 


65 


102609172 


C4746G146 


7177745!) 


66 


90271671; 


544856974 


04326110 


67 


78856225 


454585297 


57209299 


68 


68341944 


375729072 


50450081 


69 


58708049 


307387129 


440711.58 


70 


49943311 


248078479 


38101472 


71 


42026002 


198735168 


32562423 


72 


34939050 


156709166 


27476710 


73 


28661413 


121770116 


22862835 


74 


23163687 


93108703 


18729934 


75 


18411656 


69945017 


15080941 


76 


14367710 


51533361 


11913739 


77 


10985578 


37165651 


9215784 


78 


820983G 


26180073 


6963167 


79 


5983046 


17970237 


5127321 


80 


4239283 


11987191 


3668465 


81...... 


2911470 


7747908 


2542522 


82 


1931399 


4836438 


1701093 


83 


1232765 


2905039 


1094430 


84 


753859 


1072274 


074220 


85 


439734 


918416 


396000 


86 


243190 


478682 


220402 


87 


126827 


235486 


115614 


88 


61958 


108659 


56784 


89 


28143 


46700 


25920 


90 


11799 


18557 


10916 



24^ 



248 AMERICAN EXPEKIENCE TABLES. 

Table XXXII— (Concluded). 



Equal 
Ages. 

91.... 

92 ... . 

93... 

94. . .. 

95.... 

96.. .. 

97.... 

98.. . . 

99... 



^xx. 


i-^xx. 


"i-XX. 


4520.2 


6757.1 


4198.4 


1571.5 


2236.9 


1465.0 


490.03 


665.40 


458.34 


134.77 


175.37 


126.42 


32.649 


40 . 595 


30.716 


6.7384 


7.9457 


6.3600 


1.0652 


1.2073 


1.0077 


.13414 


. 14213 


.12738 


.00798 


.00798 


.00760 



TWO LIVES ANNUITIES SINGLE PREMIUMS. 249 



Table XXXIII — Two Lives. 

ANNUITIES AND SINGLE PREMIUMS PER $1. 

AMERICAN EXPERIENCE Table of Mortality, with 
Interest at 5^ Per Annum (Makehamized) . 

Equal 



10. 

11. 

12. 
13. 
14. 
15. 
16. 
17. 
18. 
19. 
20. 
21. 
22. 
23. 
24. 
25. 
26. 
27. 
28. 
29. 
30. 
31. 
32. 
33. 
34. 
35. 
36. 
37. 
38. 
39. 



Annuity. 


Single 
Premium. 


14.456734 


.2639651 


14.414628 


.2659701 


14.370314 


.2680803 


14.323328 


.2703178 


14.273481 


.2726915 


14.220857 


.2751951 


14.165369 


.2778396 


14.106718 


.2806325 


14.044724 


.2835846 


13.979478 


.2866915 


13.910441 


.2899790 


13.837676 


.2934440 


13.760932 


.2970985 


13.680265 


.3009398 


13.595088 


.3049958 


13.505421 


.3092657 


13.411288 


.3137482 


13.312392 


.3184575 


13.208412 


.3234089 


13.099006 


.32&6188 


12.984788 


.3340577 


12.864782 


.3397723 


12.738922 


.3457656 


12.607461 


.3520256 


12.469691 


.3585861 


12.326154 


.3654213 


12.176124 


.3725656 


12.019470 


.3800253 


11.856368 


.3877920 


11.687000 


.3958571 



250 



AMERICAN EXPERIENCE TABLES. 



Table XXXIII— (Continued). 

Equal Single 

Ages. Annuity. Premium. 

40 11.510588 .4042577 

41 11 . 327569 . 4129729 

42.'. 11.137442 .4220260 

43 10.940923 .4313846 

44 10.737190 .4410862 

45 10.526905 .4510998 

46 10 . 310134 . 4614222 

47 10.086617 .4720659 

48 9 . 856660 . 4830162 

49 9.620863 .4942447 

50 9.378637 .5057791 

51 9 . 130805 . 5175807 

52 8 . 877619 . 5296372 

53 8 . 619602 . 5419237 

54 8.356706 .5544426 

55 8.089691 .5671576 

56 7.818773 .5800585 

57 7.544705 .5931093 

58 7.267992 , .6062862 

59 6.989155 .6195640 

60 6 . 709012 . 6329043 

61 6 . 427917 . 6462835 

62 6.147053 .6596641 

63 5 . 866462 . 6730256 

64 5.587262 .6863208 

65 5.310022 .6995228 

66 5.035747 .7125835 

67 " 4.764736 .7254887 

68 4.497782 .7382009 

69 4.235807 .7506757 

70 3.979215 .7628944 

71- 3.728862 .7748161 

72 3.485215 .7864155 

7?, 3.248573 .7976869 

74 3.019598 .8085904 

75 2 . 798953 . 8190974 



TWO LIVES ANNUITIES ■ — SINGLE PREMIUMS. 251 



Table XXXIII— (Concluded). 

Equal Single 

Ages. Annuity. Premium. 

76 2,586748 .8292023 

77 2.383131 .8388984 

78 2.1&8867 .8481493 

79 2.003527 .8569750 

80 1.827646 .8653503 

81 1.661167 .8732775 

82 1 . 504111 . 8807568 

83 1.356524 .8877847 

84 1.218287 .8943672 

S5 1 . 088572 . 9005441 

86 0.968297 .9062715 

87 0.856744 .9115835 

88 0.753732 .9164891 

89 0.659357 .9209827 

f>0 0.572663 .9251114 

91 6.494880 .9288149 

92 . 423403 . 9322192 

J)3 0.357871 .9353393 

94 0.301210 .9380380 

95 . 243365 . 9407926 

96 . 179169 . 9438488 

97 . 133431 . 9460267 

98 0.059524 ,9495460 



252 



AMERICAN EXPERIENCE TABLES. 



Table XXXIV- 



Theee Lives — Commutation 
Columns. 



AMERICAN EXPERIENCE Table 
Interest at 6^ Per Annum ( 

Equal T-j 

Ages. ^xxx. 

10. . 61541CO0O0000OO 

.572750000000000 



N. 



11 

12.. 5.33010000000000 
1.3.. 496020000000000 

14. . 461590000000000 

15. . 429520000000000 
16.. 399060000000000 
17.. 371850000000000 
18, . 345960000000000 
19.. 321850000000000 
20.. 299390000000000 
21 . . 278480000000000 
22.. 259010000000000 
23 . . 240870000000000 
24.. 223980000000000 
25 . . 208250000000000 
26.. 193590000000000 

179940000000000 
167220000000000 
155370000000000 
144320000000000 
134030000000000 
32.. 124450000000000 
33.. 115510000000000 
107180000000000 
99410000000000 
92169000000000 
85419000000000 
79122000000000 
73246000000000 
67766000000000 
62653000000000 
57883000000000 
53427000000000 
49271000000000 
45390000000000 
41764000000000 



27. . 
28.. 
29.. 
30.. 
31.. 



34.. 
35.. 
36.. 
37.. 
38.. 
39.. 
40.. 
41.. 
42.. 
43.. 
44.. 
45.. 
46.. 



XXJr. 

8556570000000000 

7941160000000000 

7368410000000000 

r)83o400000000000 

6339380000000000 

5877790000000000 

5448270000000000 

.5048610000000000 

4676760000000000 

4330800000000000 

4008950000000000 

3709560000000000 

3451080000000000 

3172070000000000 

2931200000000000 

2707220000000000 

2498970000000000 

2305380000000000 

2125440000000000 

1958220000000000 

1802850000000000 

1658530000000000 

1524500000000000 

1400050000000000 

1284540000000000 

1177360000000000 

1077950000000000 

98.5785000000000 

900306000000000 

821244000000000 

747998000000000 

680232000000000 

617579000000000 

559696000000000 

506269000000000 

456998000000000 

411608000000000 



of Mortality, ivith 
Mahehamized). 
M 

207954200000000 

194599400000000 

18213.3200000000 

170524700000000 

159714700000000 

149625200000000 

140218500000000 

131439900000000 

123257100000000 

115621400000000 

1O84876OOOO0OOO 

101834200000000 

95625200000000 

89819010000000 

84399010000000 

79334730000000 

74591400000000 

70159970000000 

66008550000000 

62121400000000 

58469980000000 

55052360000000 

51854740000000 

48840940000000 

40011410000000 

43345220000000 

40834030000000 

38476850000000 

36247420000000 

34139130000000 

32147040000000 

30260990000000 

28474470000000 

26774800000000 

25162950000000 

23628180000000 

22163610000000 



THEEE LIVES COMMUTATION COLUMNS. 



253 



Squal 



D 



Table XXXIV— (Continued). 



Ages, 


*-':ra:a:. 


*^ XXX. 


"'^XTX. 


47.. 


38379000000000 


369844000000000 


20767380000000 


48.. 


35218000000000 


331465000000000 


19433950000000 


49.. 


32263000000000 


296247000000000 


18156000000000 


50.. 


29506000000000 


263984000000000 


16935330000000 


51.. 


26931000000000 


234478000000000 


15765380000000 


52.. 


24526000000000 


207547000000000 


14642810000000 


53.. 


22281000000000 


183021000000000 


13565710000000 


54., 


20187000000000 


160740000000000 


12532710000000 


55.. 


18235000000000 


140553000000000 


11542000000000 


56.. 


16417000000000 


122318000000000 


10592330000000 


57.. 


14724000000000 


105901000000000 


9680894000000 


58.. 


13152000000000 


91177200000000 


8810227000000 


59.. 


11694000000000 


78025200000000 


7978513000000 


60.. 


10344000000000 


06331200000000 


7185371000000 


61.. 


9098700000000 


55987200000000 


6432642000000 


62.. 


7952200000000 


46888500000000 


5719414000000 


63.. 


6902100000000 


38936300000000 


5047990000000 


64.. 


5944100000000 


32034200000000 


441966200G000 


65.. 


5074900000000 


26090100000000 


3832514000000 


06.. 


4291200000000 


21015200000000 


3290476000000 


07.. 


3590000000000 


16724000000000 


2793619000000 


68.. 


2968000000000 


13134000000000 


2342571000000 


69.. 


2421500000000 


10166000000000 


1937355000000 


70.. 


1946900000000 


7744550000000 


1578112000000 


71.. 


1539900000000 


5797650000000 


1263821000000 


72.. 


1196100000000 


4257750000000 


993349900000 


73.. 


910660000000 


3061650000000 


764867100000 


74.. 


677980000000 


2150990000000 


575551900000 


75.. 


492310000000 


1473010000000 


422100000000 


76.. 


347760000000 


980700000000 


301059700000 


77.. 


238240000000 


632946000000 


208099700000 


78.. 


157720000000 


394706000000 


138924500000 


79.. 


100550000000 


236986000000 


89264950000 


80.. 


61448000000 


, 136436000000 


54951050000 


81.. 


35837000000 


74988000000 


32266140000 


82.. 


19841000000 


39151000000 


17978670000 


83.. 


10368000000 


19310000000 


9448070000 


84.. 


5080300000 


8942400000 


4654471000 


85.. 


2319200000 


3862100000 


2135220000 


86.. 


977400000 


1542970000 


903925200 


87.. 


377180000 


565570000 


350244900 


88.. 


131970000 


188393216 


122998900 


89.. 


41399000 


56423216 


38712180 



254 



AMERICAN EXPEEIENCE TABLES. 



Equal 



Table XXXIV— (Concluded). 



M^ 



Ages. 


'-'xxx. 


'■^xxx. 


"^xxx. 


90.. 


11516000 


15024216 


10800560 


91.. 


2798000 


3508216 


2630942 


92.. 


587760 


710216 


553940 


93.. 


104870 


122456 


99038.8 


94.. 


15499 


17586 


14660.8 


95.. 


1893.6 


2087.80155 


1794.18 


96.. 


181.94 


194.20155 


172.691 


97.. 


11.717 


12.26155 


11.1331 


98.. 


.53657 


.54455 


.51064 


99.. 


.00798 


.00798 


.007600 



THBEE LIVES ANNUITIES SINGLE PREMIUMS. 255 



Table XXXV— Three Lives. 

ANNUITIES AND SINGLE PREMIUMS PER $1. 

AMERICAN EXPERIENCE Table of Mortality, tvith 
Interest at 5^ Per Annum (Makehamized) . 

Equal 



10. 

11. 

12. 
13. 
14. 
15. 
16. 
17. 
18. 
19. 
20. 
21. 
22. 
23. 
24. 
25. 
26. 
27. 
28. 
29. 
30. 
31. 
32. 
33. 
34. 
35. 
36. 
37. 
38. 
39. 





Annuity. 


Single 
Premium. 


12. 


903853 


.3379116 


12. 


864967 


.3397632 


12. 


824150 


.3417069 


12. 


,780493 


.3437859 


12. 


733790 


.3460099 


12. 


684555 


.3483544 


12. 


,632262 


.3508445 


12. 


, 577007 


.3534750 


12, 


,518210 


.3562756 


12. 


,455958 


.3592400 


12, 


,390394 


.3623621 


12, 


,320741 


.3656787 


12, 


.246902 


.3691950 


12 


.169220 


. 3728941 


12, 


.086883 


.3768149 


11 


.999856 


.3809591 


11, 


.908570 


.3853061 


11 


.811937 


.3899076 


11 


.710441 


.3947408 


11 


.603591 


.3998288 


11 


.492032 


.4051412 


11 


.374319 


.4107465 


11 


.249900 


.4166713 


11 


.120596 


.4228287 


10 


.984885 


.4292910 


10 


.843476 


.4360247 


10 


.695363 


.4430343 


10 


.540582 


. 4504484 


10 


.379465 


.4581206 


10 


.212134 


.4660887 



256 



AMERICAN EXPEKIENCE TABLES. 



Equal 

Ages. 


Table XXXV— (Continued). 

Annuity. 


Single 
Premium. 


40 


. ..: 10.037954 


.4743830 


41. . . 


9.857134 


.4829887 


42 


9.669437 


.4919315 


43 ... . 


9.475902 


.5011474 


44. ... 


9.275192 


.5107051 


45 


9.068253 


.5205592 


46 


8.855569 


.5306870 


47 


8.636624 


.5411131 


48 


8.411806 


.5518187 


49 


8.182252 


.5627499 


50 


7.946790 


.5739622 


51 


7.706621 


.5853990 


52 


7.462326 


.5970321 


53 


7.214218 


.6088466 


54.. .. 


6.962550 


.6208307 


55 


6.707869 


.6329586 


56 


6.450691 


.6452050 


57 


6.192407 


.6574908 


58 


5.932573 


.6698774 


59 


5 . 672242 


.6822741 


60 


5.412529 


.6946414 


61 


5.153319 


.7069847 


62 


4.896293 


.7192241 


63 


4.641225 


.7313702 


64 


4.389243 


.7435376 


65 


4.141008 


.7551901 


66 


3.897278 


.7667962 


67 


3.658496 


.7781669 


68 


3.425202 


.7892759 


69 


3.198224 


.8000640 


70 


2.977888 


.8105768 


71 


2.764952 


.8207163 


72 


2.559694 


.8304907 


73 


2.362012 


.8399041 


74 


2.172645 


.8489216 


75 


1.992038 


.8575097 



THREE LIVES ANNUITIES SINGLE PREMIUMS. 257 



Table XXXV— (Concluded). 

Equal Single 

Ages. Annuity. Premium. 

76 1.820066 .8657111 

77 1.656758 .8734877 

78 1.502574 .8808300 

79 1.356897 .8877668 

80 1 . 220349 . 8942691 

81 1.092474 .9003583 

82 . 973237 . 9060365 

83.. .862461 .9112728 

84 .760211 .9161803 

85 . 665278 . 9206709 

86 .578647 . 9248263 

s7 .499470 .9285882 

88 .427546 .9320217 

89 .362913 .9350994 

90 .304638 .9378743 

91 . 253830 . 9402938 

92 .208344 .9424595 

93 . 167693 . 9443959 

94 .134654 .9459191 

95 . 102557 . 9474968 

96 .067393 .9491646 

97 . 046475 . 9501664 

98 .014872 .9516745 

99 .000000 .9523810 

17 



AN ANALYSIS OP THE INHERITANCE TAX LAWS 



United States and the Various States and Territories, with 
Particular Reference to the Standards of Mortal- 
ity and Interest to be Employed in Making 
Calculations for Inheritance Tax Purposes. 



United States. 
On June 13, 1898, the Federal Collateral In- 
heritance Tax Law was enacted. Circular No. 
527, issued from the oflBce of the Commissioner 
of Internal Revenue at Washington, shows the 
rates of legacy taxes imposed on personal prop- 
erty in excess of $10,000. Although the basis for 
calculating the present value of life estates and 
remainders is not stated in the circular, the tables 
prepared by the Actuary of the Treasury Depart- 
ment are based on the Actuaries' or Combined 
Experience Table of Mortality with interest at 
the rate of 4 per cent, per annum. This act was 
repealed April 12, 1902, to take effect July 1, 1902, 
and at the present time, therefore, there is no 
Federal Collateral Inheritance Tax. 

Alabama. 
There is no Collateral Inheritance or Transfer 
Tax Law in this State. 

Arizona. 
There is no Collateral Inheritance or Transfer 
Tax Law in this Territory. 

Arkansas. 
On page 119 of the Digest of the Revenue Laws 
of this State, compiled by the Auditor of State in 
1903, will be found a reference to the inheritance 
tax laws of Arkansas, although they are appar- 
ently incorporated in the provisions relative to 

[259] 



260 INHEEITANCE TAX CALCULATIONS. 

the keeping and maintaining of ferries. Starting 
with section 352 and ending with section 364 of 
the act which was approved May 23, 1901, will be 
found the provisions pertaining to this subject. 
Section 362 is as follows : 

" Sec. 362. The value of such property as may 
be subject to said tax shall be its actual value as 
found by the court of probate, but the state treas- 
urer, or any person interested in the succession 
to said property, may apply to the court of pro- 
bate having jurisdiction of the estate, or to the 
circuit court in case there is no administration, 
and on such application said court shall ap]point 
three (3) disinterested persons who being first 
sworn, shall view and appraise such property at 
its actual market value for the purposes of said 
tax, and shall make return, thereof to the court, 
which return may be accepted by said court and 
if accepted shall be binding. And the fees of the 
appraiser shall be such as are customary in the 
administration of estates. In the case of an an- 
nuity or life estate, the value thereof shall he 
determined hy the tables of mortality employed 
by insurance actuaries and five (5) per centum 
compound interest." 

It is impossible to determine whether the mean- 
ing of the italicized portion in the preceding quota- 
tion (the italics do not appear in the original) is 
that the court of probate is authorized to use any 
of the tables of mortality which are usually em- 
ployed by insurance actuaries, or whether this is 
an unskillful reference to the specific table of 
mortality known as the Actuaries' Table. As the 
statute runs, however, calculations upon any table 
of mortality are probably acceptable to the court 
of probate which has jurisdiction in determining 
all questions relative to inheritance taxes. 

California. 
The Collateral Inheritance Tax Law of this 
State may be found on page 224 of the 1902 com- 
pilation of the Revenue Laws of the State of 



RESUME OF STATE LAWS. 261 

California. The original act was approved March 
23, 1893, took effect two months afterward, was 
amended on March 9, 1895, March 9, 1897, March 
14, 1899, and March 20, 1903. This last amend- 
ment will, of course, not be found in the com- 
pilation referred to. Section 11 gives the stand- 
ard of mortality to be used in this State, viz., the 
Actuaries' Table with 5 per cent, interest. This 
section reads as follows : 

" Sec. 11. When the value of any inheritance, 
devise, bequest, or other interest subject to the 
payment of said tax is uncertain, the Superior 
Court in which the probate proceedings are pend- 
ing, on the application of any interested party, or 
upon his own motion, shall appoint some com- 
petent person as appraiser, as often as and when- 
ever occasion may require, whose duty it shall be 
forthwith to give such notice, by mail to all per- 
sons known to have or claim an interest in such 
property, and to such persons as the court may by 
order direct, of the time and place at which he 
will appraise such property, and at such time and 
place to appraise the same and make a report 
thereof, in writing, to said court, together with 
such other facts in relation thereto as said court 
may by order require to be filed with the clerk of 
said court; and from this report the said court 
shall, by order, forthwith assess and fix the 
market value of all inheritances, devises, bequests, 
or other interests, and the tax to which the 
same is liable, and shall immediately cause notice 
thereof to be given, by mail, to all parties known 
to be interested therein; and the value of every 
future or contingent or limited estate, income, or 
interest shall, for the purposes of this Act, be de- 
termined by the rule, method, and standards of 
mortality and of value that are set forth in the 
actuaries' combined experience tables of mor- 
tality for ascertaining the value of policies of 
life insurance and annuities, and for the deter- 
mination of the liabilities of life insurance com- 
panies, save that the rate of interest to be assessed 



262 INHERITANCE TAX CALCULATIONS. 

in computing the present value of all future in- 
terests and contingencies shall be five per centum 
per annum; and the Insurance Commissioner 
shall, on the application of said court, determine 
the value of such future or contingent or limited 
estate, income or interest, upon the facts con- 
tained in such report, and certify the same to the 
court, and his certificate shall be conclusive evi- 
dence that the method of computation adopted 
therein is correct. The said appraiser shall be 
paid by the County Treasurer out of any funds 
that he may have in his hands on account of said 
tax, on the certificate of the court, at the rate of 
five dollars per day for every day actually and 
necessarily employed in said appraisement, to- 
gether with his actual and necessary traveling 
expenses." 

The 1903 amendment, referred to above, does 
not pertain to the basis of calculation. 

Colorado. 

Chapter 94 of the laws passed at the thirteenth 
session of the General Assembly of the State of 
Colorado, convened in 1901, contains the pro- 
visions apjjlicable to Inheritance Tax purposes. 
The particular section may be found on page 252 
of the official publication, and is as follows: 

' ' Sec. 33. In order to fix the value of property 
of persons whose estate shall be subject to the 
paj^ment of said tax, the county judge, on the ap- 
plication of any persons interested in the estate, 
including the state, or upon his own motion, shall 
appoint some competent person as appraiser as 
often as, or whenever occasion may require, whose 
duty it shall be forthwith to give such notice by 
mail to all persons known to have or claim an 
interest in such property, and to such persons as 
the county judge may by order direct, of the time 
and place at which he will appraise such prop- 
eity, and at such time and place to appraise the 
same at a fair market value, and for that purpose 



RESUME OF STATE LAWS. ' 263 

the appraiser is authorized by leave of the county 
judge to use subpoenas for and to compel the at- 
tendance of witnesses before him, and to take the 
evidence of such witnesses under oath concerning 
such property and the value thereof, and he shall 
make a report thereof and of such value in writ- 
ing to the county court, with the depositions of the 
witnesses examined and such other facts in rela- 
tion thereto, and to said matter as the county 
court may by order require to be filed in the 
office of the clerk of said county court, and from 
this report the said county court shall forthwith 
make an order and fix the then cash value of all 
estate, annuities and life estate or terms of years 
growing out of said estate, and the tax to which 
the same is liable, and shall immediately give 
notice by mail to all parties known to be inter- 
ested therein. Any person or persons dissatisfied 
with the appraisement or assessment may appeal 
therefrom to the district court of the proper 
county within sixty days after the making and 
filing of such appraisement or assessment, on giv- 
ing .good and sufficient security to the satisfaction 
of the county judge to pay all costs, together with 
whatever taxes that shall be fixed by the county 
court. The said appraiser shall be paid by the 
county treasurer out of any funds he may have in 
his hands on account of said tax, on the certificate 
of the county judge, at the rate of three dollars 
per day for every day actually and necessarily 
employed in said appraisement, together with his 
actual and necessary traveling expenses." 

It' will be noticed that the county court is the 
official empowered to fix the present values of the 
estates and annuities, but no provision is made 
for any table of mortality or rate of interest to 
be used in such calculations. An* inquiry ad- 
dressed to the Secretary of State elicited the in- 
formation that that official was unable to give any 
inforiiiation relative to the standards to be em- 
ployed. The statute being silent on this subject, 
it is to be assumed that the court will accept cal- 



264 INHEKITANCE TAX CALCULATIONS. 

culations made upon any recognized basis. It 
may be of interest to note that the Insurance De- 
partment of this State, which is attached to the 
Auditor of State's office, uses the Actuaries' Ex- 
perience Table of Mortality as a basis for calcu- 
lating the net present value of the outstanding 
obligations of its insurance companies. 

Connecticut. 

On June 1, 1897, the Senate and House of Eep- 
resentatives passed ' ' An Act Providing for a Suc- 
cession Tax." This is known as chapter CCI, 
and was subsequently amended by an act ap- 
proved May 6, 1903. Section 8 of the act would 
seem to place the responsibility for the calcula- 
tions in the court of probate. This section is as 
follows : 

" Sec. 8. The court of probate, having either 
principal or ancillary jurisdiction of the settle- 
ment of the estate of the decedent, shall have 
jurisdiction to hear and determine all questions 
in relation to said tax that may arise affecting 
any devise, legacy, or inheritance under this act, 
subject to appeal as in other cases, and the state 
treasurer shall represent the interests of the state 
in any such proceeding. ' ' 

It will be observed that no standard of mortality 
or rate of interest is specified. The Insurance 
Commissioner, however, uses both the Actuaries' 
and American Experience Tables of Mortality as 
a basis for calculating the present value of the 
outstanding policy obligations of the life insur- 
ance companies of his State. 

Delaware. 

Chapter 390, volume XIII of the Laws of the 
State of Delaware, passed April 8, 1869, contains 
provisions applicable to collateral taxes. The 
first eleven sections and the last nineteen have 
been repealed, but this has no practical effect 
upon the Inheritance Tax Law. The Register of 



RESUME OF STATE LAWS. 265 

Wills is the official charged with the calculation 
of the present value of life estates, annuities, 
and remainders. The act contains no reference to 
any table of mortality or rate of interest, and the 
Attorney-General under date of October, 1904, in 
an answer to an inquiry on these points, says: 
" There is no reported case in Delaware where 
interest rates and mortality tables had to be 
selected by the Court. The present incumbent of 
the office of Register of Wills states that he would, 
if the question arose before him, employ the 
American Table of Mortality and the legal rate 
of interest, which in this State is 6 per cent. I 
think you would probably be safe in stating that 
to be what would be considered the proper prac- 
tice in this State." 

DiSTEicT OF Columbia. 

There is no Inheritance or Transfer Tax Law 
upon the statute books of the District at the 
present time. A tax was imposed on inheritances 
by the War Revenue Law of 1898. This was modi- 
fied, however, by Act of Congress, dated March 2, 
1901. (See 31 Stat, at Large, § 29, page 946.) 

Florida. 

There is no Collateral Inheritance or Transfer 
Tax Law in this State. 

GrEOEGIA. 

There is no Collateral Inheritance or Transfer 
Tax Law in this State. 

Hawaii. 

There is a tax on legacies, bequests and in- 
heritances in Hawaii, and the provisions of the 
law may be found by consulting sections 910 to 
917, inclusive. This is very crude and fixes no 
standards. 



266 inheritance tax calculations. 

Idaho. 

There is no Collateral Inheritance or Transfer 
Tax Law in this State. 

Illinois. 

On page 113 of the Revenue Laws compiled by 
the Auditor in 1898 will be found the statute re- 
lating to inheritance taxes. This may also be 
found in chapter 120, paragraph 366, of the Re- 
vised Statutes of the State. Paragraph 376 has 
particular reference to our subject. This reads 
as follows: 

" 376. Row Value of Property Fixed. — Sec. 11. 
In order to fix the value of property of persons 
whose estate shall be subject to the payment of 
said tax, the county judge, on the application of 
any interested party, or upon his own motion, 
shall appoint some competent person as ap- 
praiser as often as or whenever occasion may re- 
quire, whose duty it shall be forthwith to give 
such notice by mail to all persons known to have 
or claim an interest in such property, and to such 
persons as the county judge may by order direct, 
of the time and place he will appraise such prop- 
erty, and at such time and place to appraise the 
same at a fair market value, and for that purpose 
the appraiser is authorized by leave of the county 
judge to use subpoenas for and to compel the at- 
tendance of witnesses before him, and to take the 
evidence of such witnesses under oath concerning 
such property and the value thereof, and he shall 
make a report thereof and of such value in writ- 
ing to said county judge, with the depositions of 
the witnesses examined and such other facts in 
relation thereto, and to said matter as said county 
judge may by order require to be filed in the office 
of the clerk of said county court, and from this 
report the said county judge shall forthwith use 
and fix the then cash value of all estates, annuities 
and life estates or terms of years growing out of 
said estate, and the tax to which the same is liable, 



RESUME OF STATE LAWS. 267 

and shall immediately give notice by mail to all 
parties known to be interested therein. Any per- 
son or persons dissatisfied with the appraisement 
or assessment may appeal therefrom to the county 
court of the proper county within sixty days after 
the making and filing of such appraisement or 
assessment on paj'ing the given security proof to 
the county judge to pay all costs, together with 
whatever taxes that shall be fixed by said court. 
The said appraiser shall be paid by the county 
treasurer out of any funds he may haA-e in his 
hands on account of said tax, on the certificate of 
the county judge at the rate of three dollars per 
day for every day actually and necessarily em- 
ployed in said appraisement, together with his 
actual and necessary traveling expenses." 

The county judge is required by this act to make 
the calculations, but no mortality table or rate of 
interest is specified. The Superintendent of the 
Insurance Department, however, states: " Our 
courts, however, are in the habit of using for de- 
termining the value of life estates for taxation 
purposes Dr. Wigglesworth's table (m) which has 
been adopted by the Supreme Court of Massa- 
chusetts. This is the table when 5 per cent, is the 
rate of interest. When the income is to be esti- 
mated at 6 per cent, the Northampton tables are 
used for computing the value of life interests. 
This matter you will find laid down in Puter- 
baugh 's Pleading and Practice, 1896 edition, page 
593." 

It may be stated, however, that the Wiggles- 
worth table is no longer used even in Massachu- 
setts. 

Indiana. 

There is no Collateral Inheritance or Transfer 
Tax Law in this State. 



lo 



WA. 



The taxation of collateral inheritance in this 
State is made in accordance with the provisions 



268 INHERITANCE TAX CALCULATIONS. 

of chapter 28 of the Acts of the twenty-sixth Gen- 
eral Assembly, in effect July 4, 1896, and re-en- 
acted as chapter 4, title VII, Code of 1897. The 
following sections have a direct bearing upon the 
question : 

" Sec. 1470. Remainders. — When any person 
whose estate, over and above the amount of his 
just debts, exceeds the sum of one thousand dol- 
lars shall bequeath or devise any real property to 
or for the use of the father, mother, husband, 
wife, lineal descendant, adopted child, or lineal 
descendant of such child, during life or for a term 
of years, and the remainder to a collateral heir or 
to a stranger to the blood, the court, upon the de- 
termination of such estate for life or years, shall 
upon its own motion or upon the application of 
the treasurer of state, cause such estate to be ap- 
praised at its then actual market value, from 
which shall be deducted the value of any improve- 
ments thereon, or betterments thereto, if any, 
made by the remainderman during the time of the 
prior estate, to be ascertained and determined by 
the appraisers, and the tax on the remainder shall 
be paid by such remainderman within sixty days 
from the approval by the court of the report of 
the appraisers. If such tax is not paid within 
said time, the court shall then order said real 
estate, or so much thereof as shall be necessary 
to pay such tax, to be sold." (26 G. A., chap. 28, 
§4.) 

" Sec. 1471. Life estate.— Wheneyer any real 
estate of a decedent shall be subject to such tax, 
• and there be a life estate or interest for a term 
of years given to a party other than named in the 
preceding section, and the remainder to a col- 
lateral heir or stranger to the blood, the court 
shall direct the interest of the life estate or term 
of years to be appraised at the actual market value 
thereof, and upon the approval of such appraise- 
ment by the court, the party entitled to such life 
estate, or term of years, shall within sixty days 
thereafter pay such tax, and in default thereof 



EESTJME OF STATE LAWS. 269 

the court shall order such interest in said estate, 
or so much thereof as shall be necessary to pay- 
such tax, to be sold. Upon the determination of 
such life estate or term of years, the sam& pro- 
vision shall apply as to the ascertainment oi the 
amount of the tax and the collection of the same 
on the real estate in remainder as in like cases is 
provided in the preceding section. Whenever any 
personal estate of a decedent shall be subject to 
such tax, and there be a life estate or interest for 
a term of years given to a party other than named 
in the preceding section, and remainder to a col- 
lateral heir or stranger to the blood, the court 
shall inquire into and determine the value of the 
life estate or interest for the term of years, and 
order and direct the amount of the tax thereon 
to be paid by the prior estate and that to be paid 
by the remainderman, each of whom shall pa} 
their proportion of such tax within sixty days 
from such determination, unless a longer period 
is fixed by the court, and in default thereof the 
executor, administrator or trustee shall pay the 
same out of said property, and hold the same 
from distribution, and invest it at interest under 
the order of the court until said tax is paid, or 
until the interest on the same equals the amount 
of such tax, which shall thereupon be paid." 
(Same, § 5.) 

" Sec. 1471-a. Valuation of life, term a,nd de- 
ferred estates. — The value of any estate and 
property described in sections fourteen hundred 
and seventy (1470) and fourteen hundred and 
seventy-one (1471) of the code subject to the 
collateral inheritance tax shall be determined for 
the purpose of computing said tax by the rule or 
standards of mortality and of value commonly 
used in actuaries' combined experience tables. 
The treasurer of state is directed to obtain and 
publish for the use of the courts and appraisers 
throughout the state tables showing the average 
expectancy of life, and the value of annuities or 
life and term estates, and the present worth or 



270 ISrHERITANCE TAX CALCULATIONS. 

value of remainders and reversions. The taxable 
value of life or term, deferred or future, estates 
shall be computed at the rate of four per cent 
interest. Whenever it is desired to remove the 
lien of the collateral inheritance tax on re- 
mainders, reversions, or deferred estates, parties 
owning the beneficial interest may pay at any lime 
the said tax on the present worth of such interest 
determined according to the rules herein fixed." 
(28 G.A., chap. 51, § 7.) 

It will be noticed from the above that the courts 
and appraisers are directed to use " the rule oi- 
standards of mortality and of value commonly 
used in actuaries' combined experience tables." 
it is assumed that by this is meant the Actuaries ' 
Table of Mortality, which assumption is borne out 
by the fact that the Treasurer of State has i*epro- 
duced the tables contained in Circulars 527 and 
21,231 issued by the Commissioner of Internal 
Revenue, which give the figures for an annuity of 
one dollar and single premiums for insurance of 
one dollar upon a single life on the- basis of the 
Actuaries' Table with 4 per cent, interest. It is 
needless to say that these tables are applicable to 
but few of the problems requiring solution. 

Kansas. 

There is no Collateral Inheritance or Transfer 
Tax Law in this State. 

Kentucky. 

There is no Collateral Inheritance or Transfer 
Tax Law in this State. 

Louisiana. 

On June 28, 1904, Act No. 45 was approved by 
the Governor of the State of Louisiana. This is 
an exceedingly primitive enactment which would 
seem to place the determination of the present 
T^alue of the various estates upon the different 



RESUME OF STATE LAWS. 271 

judges throughout the State exercising probate 
jurisdiction. Standards of no kind are provided 
for. 

Maine. 

Chapters 8, 9 and 10 of the Revised Statutes 
contain the laws relating to taxation. The sec- 
tions pertaining to collateral inheritance taxes are 
Nos. 69 to 85, inclusive. Section 82 shows that the 
Actuaries' Table with 5 per cent, interest is 
specified as the basis for calculation. This section 
reads as follows: 

" Sec. 82. The value of such property as may 
be subject to said tax shall be its actual market 
value as found by the judge of probate, after pub- 
lic notice or personal notice to the board of state 
assessors and all persons interested in the suc- 
cession to said property or the board of state as- 
sessors or any of said persons interested may 
apply to the judge of probate having jurisdiction 
of the estate and on such application the judge 
shall appoint three disinterested persons, who, 
being first sworn, shall view and appraise such 
property at its actual market value for the pur- 
poses of said tax, and shall make return thereof 
to said probate court, which return may be ac- 
cepted by said court in the saifie manner as the 
original inventory of such estate is accepted, and 
if so accepted it shall be binding upon the person 
by whom such tax is to be paid, and upon the 
state. And the fees of the appraisers' shall be 
fixed by the judge of probate and paid by the 
executor, administrator or trustee. In case of an 
annuity or life estate the value thereof shall be 
determined by the so-called actuaries' combined 
experience tables and five per cent compound 
interest. ' ' 

Maryland. 

The Inheritance or Transfer Tax Laws of 
Maryland are embodied in article 81 of the Code 
of Public General Laws. Sections 113 to 116, in- 
clusive, of this article were amended at the last 



272 INHERITANCE TAX CALCULATIONS. 

session of the General Assembly. The sections 
which we seek are as follows : 

' ' Sec. 133. Whenever any estate, real, personal 
or mixed, of a decedent shall be subject to the tax 
mentioned in the thirteen preceding sections, and 
there be a life estate, or interest for a term of 
years, or a contingent interest given to one party, 
and the remainder or reversionary interest to an- 
other party, the orphans' court of the county or 
city in which administration is granted, shall de- 
termine, in its discretion, and at such time as it 
shall think proper, what proportion the party en- 
titled to said life estate, or interest for a term of 
years, or contingent interest, shall pay of said 
tax; and the judgment of said court shall be final 
and conclusive ; and the party entitled to said life 
estate, or interest for a terra of years, or other 
contingent interest shall within thirty days after 
the date of such determination pay to the register 
of wills his proportion of said tax; and thereafter 
the said court shall from time to time, after the 
determination of the preceding estate, and as the 
remainder of said estate shall vest in the party 
or parties entitled in remainder or reversion, de- 
termine, in its discretion, what proportion of the 
residue of said tax shall be paid by the party or 
parties in whom the estate shall so vest; and the 
judgment of said court shall be final and each of 
the parties successively entitled in remainder or 
reversion shall pay his proportion of said tax to 
the register of wills within thirty days after the , 
date of such determination as to him; and the 
amount of said tax shall be and remain a lien 
upon such estate until the same shall be paid. 

" Sec. 134. Whenever an interest in any estate, 
real, personal or mixed, less than an absolute in- 
terest, shall be devised or bequeathed to or for the 
use and benefit of any person or object not ex- 
empted from the tax under section 120, then only 
such interest so devised or bequeathed shall be 
liable for said tax ; and it shall be the duty of the 
orphans ' court of the county or city in which ad- 



RBSUMfi OF STATE LAWS. 273 

ministration is granted, or any other court assum- 
ing jurisdiction over such administration, to de- 
termine as soon after administration is granted 
as possible, on application of such person or ob- 
ject, the value of such interest liable for said tax, 
by deducting from the whole value of the estate so 
much thereof as shall be the value of the interest 
therein of any person who, under said section 120, 
is exempt from said tax, and the residue thereof 
shall be the value of said interest upon which said 
tax is payable; and said tax so ascertained shall 
be paid by such person or object within ninety 
days from such ascertainment, with interest 
thereon at six per cent, per annum, after the ex- 
piration of twelve (12) months from the date of 
the death of the decedent, under whose will or by 
whose intestacy said interest is acquired, if said 
tax has not sooner been paid, or within ninety 
days from the time that it shall be ascertained 
that such person or object shall be entitled to any 
such interest in any estate; but such tax shall 
bear interest at the rate of 6 per cent, per annum 
from the expiration of twelve (12) months from 
said death ; but if such person or object shall fail 
to pay said tax, as above provided, then such per- 
son or object shall at the time when he, she or it 
comes into possession of such estate, pay a tax as 
provided for in said section 120, on the whole 
value thereof." 

It will be seen, therefore, that no standard of 
mortality or rate of interest is provided. 

Massachusetts. 

On page 7 of the pamphlet entitled ' ' Collateral 
Legacy and Succession Tax ' ' issued by the Treas- 
urer of the Commonwealth under date of January 
1, 1903, will be found section 16, as follows : 

" See. 16. Said tax shall be assessed upon the 
actual value of said property as found by the pro- 
bate court. Upon the application of the treasurer 
and receiver general or of any party interested 
in the succession, the probate court shall appoint 
18 



274 INHERITANCE TAX CALCULATIONS. 

three disinterested appraisers who, first being 
sworn, shall appraise such property at its actual 
market value and shall make return thereof to 
said court. Such return, when accepted by said 
court, shall be final. The fees of said appraisers, 
as determined by the judge of said court, shall be 
paid by the treasurer and receiver general. The 
value of an annuity or life estate shall be de- 
termined by the 'Actuaries' Combined Experience 
Tables ' at four per cent compound interest. ' ' 

It will be noticed that this apparently applies 
only to annuities or life estates, but it is to be 
assumed that the same standard will be employed 
in calculating remainders. 

Michigan. 

Act No. 195 of the Public Acts of 1903 contains 
the amendments to the prior act approved in 1899 
relative to inheritance taxes. The particular sec- 
tion containing directions for the calculation of 
future estates is as follows: 

" Sec. 11. The judge of probate, upon the ap- 
plication of any interested party, including the 
Auditor General and county treasurers' or upon 
his own motion, shall, as often as and whenever 
occasion may require, appoint a competent person 
as appraiser to fix the clear market value at the 
time of the transfer thereof of property which 
shall be subject to the payment of any tax imposed 
by this act, a description of which property and 
the names and residences of the persons to whom 
it passes shall be given by the judge of probate 
to such appraiser. If the property, upon the 
transfer of which a tax is imposed, shall be an 
estate, income or interest for a term of years or 
for life, or determinable upon any future or con- 
tingent estate, or shall be a remainder or rever- 
sion or other expectancy, real or personal, the en- 
tire property or fund by which such estate, income 
or interest is supported, or of which it is a part, 
^hall be appraised immediately after such trans- 



RESUME OF STATE LAWS. 275 

fer, or as soon thereafter as may be practicable, 
at the clear market value thereof as of that date : 
Provided, however, That when such estate, income 
or interest shall be of such a nature that its clear 
market value cannot be ascertained at such time, 
it shall be appraised in like manner at the time 
when such value first became ascertainable. The 
value of every future or contingent or limited 
estate, income, interest or annuity, dependent 
upon any life or lives in being, shall be determined 
by the rule, method or standard of mortality and 
value employed by the Commissioner of Insurance 
in ascertaining the value of policies of life insur- 
ance companies, except that the rate of interest 
for computing the present value of all future and 
contingent interests or estates shall be five per 
centum per annum. The Conamissioner of Insur- 
ance shall, upon request of the Auditor General, 
prepare such tables of values, expectancies and 
other matters as may be necessary for use in com- 
puting under the provisions of this act, the value 
of life estates, annuities, reversions and remain- 
ders, which shall be printed and furnished by the 
Auditor General to the several judges of probate 
upon request." 

As the Commissioner of Insurance employs the 
American Experience Table of Mortality in ascer- 
taining the present value of life insurance poli- 
cies, it is evident that the calculations for in- 
heritance tax purposes must be upon that basis 
with 5 per cent, interest. 

Minnesota. 

Chapter 103 of the General Laws of 1885 levied 
a tax upon inheritances, but this has been declared 
unconstitutional by the Supreme Court, and at 
present there is no similar act upon the statute- 
books of the State. At the Thirty-fourth Ses- 
sion of the Legislature there was introduced on 
February 13, 1905, H. F. No. 273. This was an 
Act providing for the taxation and rate of taxa- 



276 INHEBITANCE TAX CALCULATIONS. 

tion on inlieritances, devises, bequests, legacies 
and gifts, the value of which exceeds five thousand 
dollars. The tax is upon the excess only. It pro- 
vides no standards of mortality or interest rates 
for the calculation of estates, but makes the judge 
of probate the officer to determine the value of 
such inheritances, devises, bequests, etc., etc. 
When this book went to press final action had not 
been taken upon the bill. 

Mississippi. 

There is no Collateral Inheritance or Transfer 
Tax Law in this State. 

Missouri. 

Chapter 1, article XVI, Revised Statutes of Mis- 
souri, volume I, pages 185 to 193, contains the 
Collateral Inheritance Tax Law of this State. It 
may be interesting also to note that this was sus- 
tained by the Supreme Court of Missouri on Feb- 
ruary 19, 1901. Section 313 reads as follows : 

" Sec. 313. Report of appraiser to be filed in 
probate court, assessment of cash value, amount 
of tax, etc. — The report of the appraiser shall be 
filed in the office of the probate judge, and from 
such report and other proof relating to any such 
estate before the probate judge, the probate judge 
shall forthwith assess and fix the cash value of all 
estates and the amount of tax to which the same 
are liable ; or the probate judge may so determine 
the cash value of all such estates and the amount 
of the tax to which the same are liable without 
appointing an appraiser. The value of every 
limited estate, income, interest or annuity de- 
pendent upon any life or lives in being shall be 
determined by the rule, method and standards of 
mortality and value, which are employed by the 
superintendent of the insurance department in 
ascertaining the value of policies of life insurance 
and annuities, save that the rate of interest for 
computing the value of such estates or interest 



EfiSUME of" state LAWS. 277 

shall be five per centum per annum; and the su- 
perintendent of the insurance department shall, 
on the application of any probate judge, determine 
the value of such limited estates or interests upon 
the facts contained in such report, and certify the 
game to the probate judge, and his certificate shall' 
be conclusive evidence that the method of com- 
putations adopted therein is correct. Any person 
dissatisfied with the appraisement or assessment 
and determination of tax, may appeal therefrom 
to the probate judge within sixty days from the 
fixing, assessing and determination of the tax, by 
the probate judge as herein provided, upon filing 
in the office of the probate judge a written notice 
of appeal, which shall state the grounds upon 
which the appeal is taken and on paying or giving 
security, approved by the probate judge, to pay 
all costs of the jproceeding. The probate judge 
shall immediately give notice, upon the determina- 
tion by him as to the value of any estate which is 
taxable under this article and of the tax to which 
it is liable, to all persons known to be interested 
therein." (New section.) 

The Superintendent of Insurance in this State 
uses the Actuaries' Table of Mortality which, 
therefore, is the basis for inheritance tax calcula- 
tions with 5 per cent, interest. It may also be 
interesting to note the following which appears in 
the digest of the law: 

" Each Shake Appraised, Not the Estate in 
. General. 

" The probate judge or the appraiser does not 
fix a value upon the entire estate, but upon the 
share passing to each heir, legatee or devisee, as 
the case may be. In ascertaining such share, it 
will be necessary (Sec. 312) to deduct the debts 
of the deceased (as far as they can be ascer- 
tained), and the costs of administration; and de- 
termine the Clear Market Value of the share of 
each person entitled to distribution. The tax is 
imposed upon such individvM share." 



278 inheritance tax calculations. 

Montana. 

No data can be obtained relative to the stand- 
ards employed in this State. 

Nebraska. 

The Inheritance Tax Law in this State is chap- 
ter 54 of the Laws of 1901 and was approved 
April 1st. The county judges are the ones au- 
thorized to determine the present value of estates^ 
but there are no standards fixed by law either as 
to mortality or interest. The Auditor of State, 
however (who is in charge of the insurance in- 
terests), uses the Actuaries' and American Tables 
of Mortality as a basis for valuing the outstand- 
ing insurance contracts in his State. 

Nevada. 

There is no Collateral Inheritance or Transfer 
Tax Law in this State. 

New Hampshire. 

There is no Inheritance or Transfer Tax Law 
upon the statute-books of New Hampshire at 
present, inasmuch as the law was declared un- 
constitutional a few years ago but the Constitu- 
tion was amended in 1903 to avoid objection. 
Since that date, however, no legislation has been 
enacted. 

New Jersey. 

Chapter 210 of the Laws of 1894 contains the. 
provisions relative to inheritance taxes. Section 
13 reads as follows : 

" Sec. 13. And be it enacted, That in order to 
fix the value of property of persons whose estates 
shall be subject to the payment of said tax, the 
surrogate or register of the prerogative court, on^ 
the application of any interested party, or upon 
his own motion, shall appoint some competent per- 
son as appraiser as often as, and whenever occa- 
sion may require, whose duty it shall be forthwith 



RESUME OF STATE ^AWS. 279 

to give such notice by mail, and to such persons as 
the surrogate or register of the prerogative court 
may by order direct, of the time and place he will 
appraise such property, and at such time and 
place to appraise the same at its fair market 
value, and make a report thereof in writing to 
sRid surrogate or register of the prerogative 
court, together with such other facts in relation 
thereto as said surrogate or register of the pre- 
rogative court may by order require, to be filed 
in the office of such surrogate or register of the 
prerogative court, and from this report the said 
surrogate or register of the prerogative court 
shall forthwith assess and fix the then cash value 
of all estates, annuities and life estates, or term of 
years growing out of said estates, and the tax to 
which the same is liable, and shall immediately 
give notice thereof by mail to the state comptrol- 
ler and to all parties known to be interested 
therein; any person or persons dissatisfied with 
said appraisement or assessment may appeal 
therefrom to the ordinary or orphans' court of 
the proper county, within sixty days after the 
making and filing of such assessment, on pajdng 
or giving security, approved by the ordinary or 
orphans' court, to pay all costs, together with 
whatever tax shall be fixed by said court ; the said 
appraiser shall be paid by the state treasurer on 
the warrant of the comptroller, on the certificate 
of the ordinary or surrogate, duly filed with the 
comptroller, at the rate of three dollars per day 
for every day actually and necessarily employed 
in said appraisement, together with his actual and 
necessary traveling expenses." 

The Commissioner of Banking and Insurance 
uses the Actuaries ' Table of Mortality and the 
American Experience in the valuation of policies. 
♦ 

New Mexico. 

There is no Collateral Inheritance or Transfer 
Tax Law in this State. 



280 inhekitance tax caiictjlations. 

New Yokk. 

Article X of chapter 908, Laws of 1896, known 
as the Tax Law, and chapter XXIV of the Gen- 
eral Laws, as amended, furnish the basis for levy- 
ing inheritance tttxes in New York. The partic- 
ular section in which we are interested is as 
follows : 

" The value of every future or limited estate, 
income, interest or annuity dependent upon any 
life or lives in being shall be determined by the 
rule, method and standard of mortality and value 
employed by the superintendent of insurance in 
ascertaining the value of policies of life insurance 
and annuities for the determination of liabilities 
of life insurance companies, except that the rate 
of interest for making such computation shall be 
five per centum per annum. In estimating the 
value of any estate or interest in property, to the 
beneficial enjoyment or possession whereof there 
are persons or corporations presently entitled 
thereto, no allowance shall be made in respect of 
any contingent incumbrance thereon, nor in re- 
spect of any contingency upon the happening of 
which the estate or property or some part thereof 
or interest therein might be abridged, defeated or 
diminished. ' ' 

The laws pertaining to the mortality standards 
which the Superintendent of Insurance may use 
in that State are very vague, and as an actual 
fact the Superintendent employs a number of 
standards in his various valuations. An examina- 
tion of the certificates which he has issued, shows 
conclusively that he employs the American Ex- 
perience Table of Mortality with 5 per cent, 
interest. 

NOBTH CaEOLINA. 

The Inheritance Tax Law in this State is part 
of the Revenue and Machinery Acts. Schedule 
AA pertains particularly to inheritance tax mat- 
ters and may be found on page 4 of the 1903 com- 
pilation of these Acts. Section 15 is as follows: 



RESUME OF STATE LAWS. 281 

" Sec. 15. Appraiser to be appointed by the 
Clerk, etc. — It shall be the duty of the Clerk of 
the Court of the county in which letters testa- 
mentary or of administration are granted to ap- 
point an appraiser, as often as, and whenever 
occasion may require, to fix the valuation of es- 
tates which are or shall be subject to inheritance 
tax, and it shall be the duty of said appraiser to 
make a fair and conscionable appraisement of 
such estates; and it shall further be the duty of 
such appraiser to assess and fix the cash value of 
all annuities and life estates growing out of said 
estates, upon which annuities and life estate the 
inheritance tax shall be immediately payable out 
of the estate at the rate of such valuation : Pro- 
vided, that any person or persons not satisfied 
with said appraisement shall have the right to ap- 
peal within sixty days to the Court of the proper 
county on paying or giving security to pay all 
costs, together with whatever tax shall be fixed by 
said Court, and upon such appeal said Court shall 
have jurisdiction to determine all questions of 
valuation and of the liability of the appraised 
estate for such tax, subject to the right of appeal 
to the Supreme Court, as in other cases. The 
compensation of appraisers appointed under this 
act shall be at the rate of three dollars per day for 
each day necessarily employed in making the ap- 
praisement, together with such necessary travel- 
ing expenses as may be incurred, a statement of 
which shall be properly itemized and sworn to, 
subject to the final approval of the Auditor of 
State before payment is made by the Clerk of the 
Court." 

This paragraph imposes upon appraisers the 
duty of determining the present values of life 
estates, but specifies no standards. It is stated, 
however, that the American Experience Table of 
Mortality is allowed to be introduced in the courts 
as evidence and is generally followed, and the 
legal rate of interest in the State is 6 per cent. 

By an Act ratified March 2, 1905, the General 



282 INHEBITANCE TAX CALCULATIONS. 

Assembly enacted "An Act to facilitate the cal- 
culation, of the present worth of annuities." This 
attempts to give a table which will show the 
present worth or cash value of a life estate. It 
merely gives the present value of one dollar per 
annum for a various number of years from one to 
fifty. The method adopted in using this table is 
to ascertain the expectation of life of the life ten- 
ant and then to find the present value of one dollar 
per annum for that number of years. It is need- 
less to say that this is entirely incorrect and leads 
to serious discrepancies. 

North Dakota. 

At the Eighth Session of the Legislative Assem- 
bly a bill for the assessment and collection of 
collateral succession or inheritance taxes was 
passed and approved March 10, 1903. Part of 
section 10 is of interest to us as referring to our 
subject : 

" Sec. 10. Life estate. — Whenever any real es- 
tate of a decedent shall be subject to such tax, and 
there be a life estate or interest for a term of 
years given to a party other than named in the 
preceding section, and the remainder to a col- 
lateral heir or stranger to the blood, the court 
shall direct the interest of the life estate or term 
of years to be appraised at the actual market 
value thereof, and, upon the approval of such 
appraisement by the court, the party entitled to 
such life estate or term of years, shall within 
sixty days thereafter pay such tax, and in default 
thereof the court shall order such interest in said 
estate, or so much thereof as shall be necessary 
to pay such tax, to be sold. Upon the determina- 
tion of such life estate or term of years, the same 
provision shall apply as to the ascertainment of 
the amount of the tax and the collection of the 
same on the real estate in remainder as in like 
cases is provided in the preceding section." 

No standards of mortality or interest, however, 
are specified. 



besum:e of state laws. 283 

Ohio. 

The " Russell Inheritance Tax Law," as it is 
inown, was approved April 25, 1904. Section 9 
is as follows : 

" Sec. 9. The value of such property as ma> 
be subject to such tax shall be its actual market 
value, as found by the court of probate; but the 
state, through the attorney-general, or the prose- 
cuting attorney of the county when directed by 
the attorney-general, or any person interested in 
the succession to said property may apply to the 
court of probate having jurisdiction of the es- 
tate; and on such application the court shall ap- 
point three disinterested persons, who, being first 
sworn, shall view and appraise such property at 
its actual market value for the purpose of said 
tax, and shall make return thereof to said court, 
which return may be accepted by said court in 
the same manner as the original inventory of such 
estate is accepted, and if so accepted it shall be 
binding upon the person by whom this tax is to 
be paid, and upon the state. The fees of the ap- 
j)rg,isers shall be fixed by the judge of probate 
and paid out of such tax by the auditor of state. 
In case of an annuity or life estate, the value 
thereof shall be determined by the so-called actu- 
aries' combined experience tables and five per 
■centum compound interest." 

It will be seen from this that the Actuaries' 
Table of Mortality with 5 per cent, interest is the 
standard. 

Oklahoma. 

There is no Collateral Inheritance or Transfer 
Tax Law in -this Territory. 

Okbgon. 

By an act approved February 16, 1903, taxes 
were levied upon gifts, legacies, and inheritances. 
Section 22 is as follows: 

" Sec. 22. Immediate appraisal, when. — Every 
inheritance, devise, bequest, legacy, or gift, upon 



284 INHEKITANCE TAX CALCULATIONS. 

wMch a tax is' imposed under this title, shall 
be appraised at its full and true value imme- 
diately upon the death of the decedent, or as 
soon thereafter as may be practicable: Pro- 
vided, however, that when such devise, bequest, 
legacy, or gift shall be of such a nature that its 
full and true value cannot be ascertained at such 
time, it shall be appraised in like manner at the 
time when such value first becomes ascertainable. 
The value of every future or contingent or limited 
estate, income, interest, or annuity dependent 
upon any life or lives in being shall be determined 
by the rules or standard of mortality, and of value 
commonly used by actuaries ' combined experience 
tables, except that the rates of interest on com- 
puting the present value of all future and con- 
tingent interests or estates shall be four per cen- 
tum per annum interest." 

It will be seen from this that the Combined Ex- 
perience Table of Mortality with 4 per cent, in- 
terest is the standard. 

Pennsylvania. 

By an act approved ^laj 6, 1887, the Senate and 
House of Representatives enacted the inheritance 
tax laws of the State of Pennsylvania. The fol- 
lowing sections are to be noted : 

" Sec. 3. In all cases where there has been or 
shall be a devise, descent or bequest to collateral 
relatives or strangers, liable to the collateral in- 
heritance tax, to take effect in possession, or come 
into actual enjoyment after the expiration of one 
or more life estates, or a period of years, the tax 
on such estate shall not be payable,, nor interest 
begin to run thereon, until the person or persons 
liable for the same shall come into actual posses- 
sion of such estate, by the termination of the es- 
tates for life or years, and the tax shall be as- 
sessed upon the value of the estate at the time the 
right of possession accrues to the owner as afore- 
said : Provided, That the owner shall have the 
right to pay the tax at any time prior to his com- 



RESUME OF STATE LAWS. 285 

ing into possession, and in such cases, the tax 
shall be assessed on the value of the estate at the 
time of the payment of the tax, after deducting 
the value of the life estate or estates for years : 
And provided further, That the tax on real estate 
shall remain a lieii on the real estate on which 
the same is chargeable until paid. And the owner 
of any personal estate shall make a full return of 
the same to the register of wills of the proper 
county within one year from the death of the de- 
cedent, and within that time enter into security 
for the payment of the tax to the satisfaction of 
such register ; and in case of failure so to do, the 
tax shall be immediately payable and collectible. ' ' 

" Sec. 12. It shall be the duty of the register 
of wills of the county in which letters testament- 
ary, or of administration, are granted, to appoint 
an appraiser as often as, and whenever occasion 
may require, to fix the valuation of estates which 
are, or shall be, subject to collateral inheritance 
tax, and it shall be the duty of such appraiser to 
make a fair and conscionable appraisement of 
such estates, and it shall further be the duty of 
such appraiser to assess and fix the cash value 
of all annuities and life estates growing out of 
said estates, upon which, annuities and life es- 
tates the collateral inheritance tax shall be im- 
mediately payable out of the estate at the rate 
of such valuation: Provided, That any person 
or persons not satisfied with said appraisement 
shall have the right to appeal, within thirty days, 
to the orphans' court of the proper county or 
city, on paying, or giving security to pay, all 
costs, together with whatever tax shall be fixed 
by said court, and upon such appeal said court 
shall have jurisdiction to determine all questions 
of valuation, and of the liability of the appraised 
estate for such tax, subject to the right of appeal, 
to the supreme court as in other cases." 

No provision exists here for the table of mortal- 
ity or rate of interest which is to be used. A 
communication from the Auditor-General of the 



286 INHERITANCE TAX CALCULATIONS. 

Commonwealth, however, states that the Register 
of Wills is the authorized agent of the Common- 
wealth for the collection of collateral inheritance 
taxes, and while the laws do not designate any 
particular table of mortality, the Carlisle has been 
generally accepted as the basis for determining 
the value of life estates, annuities, etc. The legal 
rate in the Commonwealth is 6 per cent., although, 
because it has been more convenient, owing to 
the existence of some previously prepared table, 
the 5 per cent, basis has been used in some coun- 
ties. 

Rhode Island. 

There is no Collateral Inheritance or Transfer 
Tax Law in this State. 

South Carolina. 

There is no Collateral Inheritance or Transfer 
Tax Law in this State. 

South Dakota. 

There is no Collateral Inheritance or Transfer 
Tax Law in this State. 

Tennessee. 

The provisions relative to inheritance taxes in 
this State may be found on page 150 of the 1903 
Digest of the Tennessee Tax Laws, being chapter 
174 of the Acts of 1893. Section 12 is as follows : 

" Sec. 12. Be it further enacted, That it shall 
be the duty of the Clerk of the County Court in 
which letters testamentary or of administration 
are granted to appoint an appraiser, as often 
as and whenever occasion may require, to fix 
the valuation of estates which are or shall be 
subject to collateral inheritance tax; and it 
shall be the duty of such appraiser to make a 
fair conscionable appraisement of such estates, 
and it shall further be the duty of such ap- 
praiser to assess and fix the cash value of all 



eesum:e of state laws. 287 

annuities and life estates growing out of said 
estates, upon which annuities and life estates the 
collateral inheritance tax shall be immediately 
payable, out of the estate, at the rate of such 
valuation, but shall bear no interest till the lapse 
of twelve months from the death of the decedent ; 
and in fixing the value of such annuities and life 
estate the computation shall be made by the Car- 
lisle Life Table, whenever the use of life tables 
is necessary or applicable." 

This is peculiar, inasmuch as it specifies the 
table of mortality, but provides no rate of interest. 
The Comptroller of the State, however, advises 
that the legal rate of interest and the one used 
in all calculations in the State of Tennessee, is 
6 per cent. 

Texas. 

There is no Collateral Inheritance or Transfer 
Tax Law in this State. 

Utah. 

The Inheritance Tax Law of this State will bb 
found on page 61 of the Session Laws of 1901, 
and sections 1 and 11 are amended on page 77 of 
the Laws of Utah of 1903. No provision is made 
for either a table of mortality or rate of interest, 
and the Secretary of State advises that these 
questions have not yet been determined by the 
courts of the State. 

Vermont. 

By an act approved November 24, 1896 (No. 
46), taxes were imposed upon collateral inherit- 
. ances. Section 8 reads as follows : 

" Sec. 8. The value of such property as may 
be subject to, said tax shall be its actual market 
value as found by the judge of probate ; but the 
commissioner of state taxes, in person may, or 
the state's attorney of the county where the es- 
tate is being settled when by the commissioner 
directed shall, or any person interested in the 



288 INHERITANCE TAX CALCULATIONS. 

succession to said property, may apply to the 
judge of probate having jurisdiction of the es- 
tate, and on such application the judge shall ap- 
point three disinterested persons, who, being first 
sworn, shall view and appraise such property at 
its actual market value for the purposes of said 
tax, and shall make return thereof to said Pro- 
bate Court, which return may be accepted by said 
court in the same manner as the original inventory 
of such estate is accepted, and if so accepted it 
shall be binding upon the person by whom this 
tax is to be paid, and upon the State. And the 
fees of the appraisers shall be fixed by the judge 
of probate and paid by the executor, administra- 
tor or trustee. In case of an annuity or life es- 
tate the value thereof shall be determined by the 
so called actuaries' combined experience tables 
and five per cent, compound interest." 

The Combined Experience Table of Mortality 
with 5 per cent, interest is, therefore, the stand- 
ard in this State. 

Virginia. 

The Collateral Inheritance Tax Law in Vir- 
ginia was approved April 16, 1903. It is exceed- 
ingly primitive and contains no specification as 
to the table of mortality or rate of interest which 
is to be used. In response to an inquiry, how- 
ever, the Secretary of the Commonwealth advises 
that the Carlisle Table with interest at 6 per cent, 
is recognized as the legal basis in Virginia. 

Washington. 

Chapter IV, approved March 6, 1901, contains 
the provisions relative to the taxation of inherit- 
ances. A portion of section 8 is applicable to 
our purposes: 

" Sec. 8. Whenever any real estate of a dece- 
dent shall be subject to such tax, and there be a 
life estate or interest for a term of years given 
to a party other than the father, mother, husband, 



RESUME OF STATE LAWS. 289 

wife, lineal descendant, adopted child, or lineal 
descendant of such child, and the remainder to a 
collateral heir or stranger to the blood, the court 
shall direct the interest of the life estate or term 
of years to be appraised at the actual value 
thereof according to the rules or standards of 
mortality and of value commonly used in actu- 
aries' combined experience tables. The State 
Treasurer is directed to obtain and publish for 
the use of the courts and appraisers throughout 
the state, tables showing the average expectancy 
of- life, and the value of annuities or life and term 
estates, and the present worth or value of remain- 
ders and reversions. The taxable value of life or 
term, deferred or future estates, shall be com- 
puted at the rate of four per cent, per annum 
interest." 

The Combined Experience Table of Mortality, 
therefore, with 4'per cent, interest, is the standard 
jn this State. ' 

West "Virginia. 

Chapter; 6, enacted by th^ Legislature of this 
State a,t its Extraordinary , Session commencing 
July 26, 1904, provides foi" the levying and col- 
lection of collateral inheritance taxes. This act 
went into effect at the expiration, of ninety days 
from its passage, August 8, 10(34. Section 5 is 
as follows: . , , , 

' ' Sec. 5. Whenever the transfer of any prop- 
erty shall be subject to tax hereunder 3,nd. only a 
life estg,te^, or an interest for a term of years, or 
a contingent interest to be transferred to one 
person and th^ remainder or reyersiona,ry inter- 
est to another^ the state tax commissioner on the 
application of any person in interest, or upon his 
own motion, may, after dne notice to the persons 
interested, apportion siich taxes among such per- 
sons and assess to each of them his proper share 
of such taxes, and shall make his certificates ac- 
cordingly, which shall be forwarded and disposed 
of in the same manner as other certificates by him 
herein provided for. The portion of any such 
19 



290 INHERITANCE TAX CALCULATIONS. 

taxes apportioned to any person entitled in re- 
mainder or reversion shall be payable at once, 
and such person shall be required to pay them in 
the same manner, and within the same time, as 
if his interest had vested in possession." 

■This, it will be seen, specifies no table of mor- 
tality or rate of interest, and the Auditor of State 
advises that the courts have never passed upon 
the question, and no basis has, therefore, legally 
been established. 

Wisconsin. 

The provisions relating to inheritance taxes in 
this State may be found in chapter 44 of the Laws 
of 1903. The Commissioner of Insurance is 
charged with the calculation of future estates, as 
follows : 

"Transfer where tax imposed. (2) Whenever a 
transfer of property is made upon which there 
is, or in any contingency ther^ may be, a tax im- 
posed, such property shall be appraised at its 
clear market value immediately upon the trans- 
fer or as soon thereafter as practicable. The 
value of every future or limited estate, income, 
interest or annuity dependent upon any life or 
lives in being, shall be determined by the ru:0, 
method and standard of mortality and value em- 
ployed by the commissioner of insurance in ascer- 
taining the value of policies of life insurance and 
annuities for the determination of liabilities of 
life insurance companies except that the rate of 
interest for making such computation shall be five 
per centum per annum." 

The standard of mortality in this State being 
the American Experience, it follows that that is 
the one used by the Commissioner of Insurance 
in inheritance tax calculations, with interest at 
the rate of 5 per cent, per annum. 

Wyoming. 

A bill for taxing gifts, legacies, and inherit- 
ances in this State was introduced January 30, 



EfeUMilB OF STATE LAWS. 291 

1903, passed and approved February 21, 1903. 
Section 11 is as follows : 

' ' Sec. 11. In order to fix the value of property 
of persons whose estate shall be subject to the 
payment of said tax, the district judge," on the ap- 
plication of any persons interested in the estate, 
including the state, or upon his own motion, shall 
appoint some competent person as appraiser as 
often as, or whenever occasion may require, whose 
duty it shall be forthwith to give notice by mail 
to all persons known to have or claim an interest 
in such property, and to such persons as the dis- 
trict judge may by order direct, of the time and 
place at which he will appraise such property, 
and at such time and place to appraise the same 
at a fair market value, and for that purpose the 
appraiser is authorized by leave of the district 
judge to use subpoenas for and to compel the 
attendance of witnesses before him, and to take 
evidence of such witnesses under oath concerning 
such property and the value thereof, and he shall 
make a report thereof and of such value in writ- 
ing to the district court with the depositions of 
the witnesses examined and such other facts in 
relation thereto as the district court may by order 
require to be filed in the office of the clerk of said 
district court, and from this report the said dis- 
trict court shall forthwith make an order and fix 
the then cash value of all estate, annuities and 
life estates or terms of years growing out of said 
estate, and the tax to which the same is liable, 
and shall immediately give notice by mail to all 
parties known to be interested therein. Any per- 
son or persons dissatisfied with the appraisement 
or assessment may appeal therefrom to the dis- 
trict court of the proper county within sixty days 
after the making and filing of such appraisement 
or assessment, on giving good and sufficient se- 
curity to the satisfaction of the district judge to 
pay all costs together with whatever taxes that 
shall be fixed by the district court. The said ap- 
praiser shall be paid by the county treasurer out 



292 INHEKITANCE TAX CALCULATIONS. 

of any funds he may have in his hands on account 
of said tax, on the certificate of the district judge 
at the rate of three dollars per day for every day 
actually and necessarily employed in said ap- 
praisement together with his actual and neces- 
sary traveling expenses, and the witnesses sub- 
poenaed by said appraiser shall be paid such fees 
as now provided by law. ' ' 

The act specifies no table of mortality or rate of 
interest. 



KEY TO NOTATION. 



Ow = the present value of an annuity, payable during 
the life of a person now aged x, the first pay- 
ment to be made one year from date. This 
symbol is also used to indicate the present value 
of the interest of a life tenant now aged x in an 
estate. 

Owy = the present value of an annuity, payable during 
the joint existence of two individuals now aged 
X and y respectively, the first payment to be 
made one year from date. This symbol is also 
used to indicate the present value of the in- 
terest which two beneficiaries have in an estate, 
the income of which is payable to them during 
their joint existence. 

Oxyi =^ the present value of an annuity, payable during 
the joint existence of three individuals now aged 
X, y and z respectively, the first payment to be 
made one year from date. This symbol is also 
used to indicate the present value of the interest 
of three individuals in an estate, the income of 
which is payable during their joint existence. 

o 

a = the present value of a complete annuity, i. e., one 
payable but once each year, but in the event of 
the death of the annuitant a proportionate pay- 
ment is made to his estate for the period elapsing 
between the last periodic payment and the date 

of death. 

[293] 



294 KEY TO NOTATION. 

a^J^ = the present value of ax when the payments are 
made in semi-annual installments instead of 
annually. 

L== number living at^any age x. 

dx = number dying at any age x. 

i = the effective rate of interest, i. e., the interest on a 
unit of money actually realized in a year. 

l+i=the amount of one unit of money at i rate of 
interest at the end of one year. 



^the present value of one unit of money 



1 + i 

discounted for one year at i rate of interest. 

-- V For the explanation of these two symbols see 

Chapter IV. 

C ) 

[■ For the explanation of these two symbols see 

Chapter VII. 

Aif = the present value of an insurance, payable at the 
end of the year in which the death of an indi- 
vidual now aged x occurs. This symbol is also 
used to represent the present value of the re- 
mainder which will vest upon the death of a 
life tenant now aged x. 

A«» = the present value of an insurance, payable at the 
end of the year in which the first death occurs 
among two designated individuals now aged x 
and y respectively. This symbol is also used to 
designate the present value of the remainder 
which vests at the first death among two desig- 
nated individuals now aged x and y. 



KEY TO NOTATION. 295 

i^x = the force of mortality = " the proportion of per- 
sons at age x who would die in a year if the 
intensity of mortality remained constant for. a 
year and if the number of persons under ob- 
servation also remained constant, the places of 
those who die being constantly occupied by fresh 
lives." 



INDEX. 



P»ge- 

Actuaries' experience table of morality 3, 182 

Alabama, Inheritance Tax Law of 259 

American experience table of mortality 3, 237 

Annuity certain 48 

Annuity, deferred, single life, derivation of formula for. . . . 18 

Annuity, one life, derivation of formula for 14 

Annuity, temporary, single life, derivation of formula for. . 17 

Arizona, Inheritance Tax Law of 259 

Arkansas, Inheritance Tax Law of 259 

Barrett, George 14 

Bequest, present value of 71 

California, Inheritance Tax Law of 260 

Carlisle table of mortality 2, 143 

Colorado, Inheritance Tax Law of ." 262 

Combined experience table of mortality 3, 182 

Commutation columns, explanation of 14 

Complete annuity or life estate 42 

Compound interest 8 

Computation of expectation of life, method of 7 

Connecticut, Inheritance Tax Law of 264 

Curtate annuity or life estate 42 

Curtesy, present value of estate by 51 

Dale, William 14 

Davies, Griffith 14 

Delaware, Inheritance Tax Law of 264 

Determination of present value of $1 8 

Discount 7 

Discount tables 84 

District of Columbia, Inheritance Tax Law of 265 

Dower, present value of 50 

Dower right, present value of 95 

Equal ages method 35 

Estate, survivorship 52 

Estate for term of years, present value of 47 

Expectancy of life 7 

[297] 



298 INDEX. 

Page. 

Falcidian law 1 

Federal Inheritance Tax Law 259 

First American mortality observation 3 

First mortality table 1 

Florida, Inheritance Tax Law of 265 

Force of mortality 26 

Force of mortality tables 87 

Georgia, Inheritance Tax Law of 265 

Graduated American experience table of mortality 22 

Graduated Carlisle table of mortality 22 

Hawaii, Inheritance Tax Law of 265 

Homans, Sheppard 3 

Hunter, Arthur 22 

Idaho, Inheritance Tax Law of 266 

Illinois, Inheritance Tax Law of 266 

Inchoate dower right 58 

Inchoate dower right, formula for 20 

Indiana, Inheritance Tax Law of 267 

Inheritance tax laws, analysis of 259 

Interest 7 

Interest factor 3 

Interest tables 81 

Iowa, Inheritance Tax Law of 267 

Joint annuity, temporary, two lives, derivation of formula 

for 22 

Joint annuity, three lives, derivation of formula for 22 

Joint annuity, two lives, derivation of formula for 21 

Joint deferred annuity, two lives, derivation of formula for. . 23 

Joint estate, present value of 51 

Joint life insurance 35 

Joint and survivorship estates 55, 57 

Kansas, Inheritance Tax Law of 270 

Kentucky, Inheritance Tax Law of 270 

Legacy, present value of 71 

Life estate, deferred 53 

Life estate, deferred, three lives. .60, 61, 63, 64, 65, 66, 67, 68, 69 

Life estate, joint, three lives 58, 59 

Life estate, postponed enjoyment of 48 

Life estate, postponed enjoyment and continuance for tem- 
porary period of 49 

Life estate, present value of 47, 95 



iNDEi. 299 

Page. 

Life estate, single life, derivation of formula for 14 

ijoulsiana, Inheritance Tax Law of 270 

Maine, Inheritance Tax Law of 27 1 

Jfakehamized American table (force of mortality) 87 

Makehamized Carlisle table (force of mortality 87 

Maryland, Inheritance Tax Law of 271 

Massachusetts, Inheritance Tax Law of 273 

Michigan, Inheritance Tax Law of 274 

.Milne, Joshua ,2 

Minnesota, Inheritance Tax Law of 275 

Mississippi, Inheritance Tax Law of 276 

Missouri, Inheritance Tax Law of 276 

Montana, Inheritance Tax Law of 278 

Mutual Life Insurance Company, experience 3 

Nebraska, Inheritance Tax Law of 278 

Nevada, Inheritance Tax Law of 278 

New Hampshire, Inheritance Tax Law of 278 

New Jersey, Inheritance Tax Law of 278 

New Mexico, Inheritance Tax Law of 279 

New York, Inheritance Tax Law of 280 

Northampton table of mortality 2, 90 

North Carolina, Inheritance Tax Law of 280 

North Dakota, Inheritance Tax Law of 282 

Number living : 10 

Ohio, Inheritance Tax Law of 283 

Oklahoma, Inheritance Tax Law of 283 

Oregon, Inheritance Tax Law of 283 

Pennsylvania, Inheritance Tax Law of 284 

Present value, determination of 8 

Price, Doctor 2 

Principal rates of interest •. 3 

Probability of death 32 

Remainder, contingent 37, 74 

Remainder, present value of 70, 72, 73, 95 

Remainder, vested 32 

Rhode Island, Inheritance Tax Law of 286 

Single premium 95 

South Carolina, Inheritance Tax Law of 286 

South Dakota, Inheritance Tax Law of 286 

iSurvivorship annuities 23 

Survivorship estate 52 



300. INDEX. 

Page. 

Tennessee, Inheritance Tax Law of .\ 280 

Tetens, John Nicholas 14 

Texas, Inheritance Tax Law of 287 

.•>IUI 

Ulpianus .(.,,! 1 

Utah, Inheritance Tax Law of •. 287 

Vermont, Inheritance Tax Law of '.".\*'.V'. .".'j. . 287 

Vested remainder '...'. "'."'..'. '.'.'."I':': . 70 

Virginia, Inheritance Tax Law of . .".'.'/.". 288 

Washington, Inheritance Tax Law of 288 

West Virginia, Inheritance Tax Law of :! 289 

Wigglesworth, Edward 2 

Wisconsin, Inheritance Tax Law of 290 

Wyoming, Inheritance Tax Law of , , . 290 

[Whole Numbek of Pages 308 J 






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